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Problems on Ages

মোট প্রশ্ন৬০৭এই পাতা১০০প্রতি পাতা১০০
প্রশ্ন দেখুনঅনুশীলন
ঘনত্ব
উত্তর
উত্তরিতবর্তমানপুনরায় দেখুনঅসম্পূর্ণ

Problems on Ages

PrepBank · পাতা ৪ / ৭ · ৩০১–৪০০ / ৬০৭

৩০১.
The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?
  1. ক
    12
  2. খ
    13
  3. গ
    14
  4. ঘ
    15
ব্যাখ্যা
Question: The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?

Solution:
Here,
(A + B) - (B + C) = 12
∴ A - C = 12.

∴ C is younger than A by 12 years.
৩০২.
Fahim is as much younger than Bilash as he is older than Wasim. If the sum of the ages of Wasim and Bilash is 66 years, then what is definitely the difference between Fahim’s and Wasim's age?
  1. ক
    ক) 18
  2. খ
    খ) 16
  3. গ
    গ) 15
  4. ঘ
    ঘ) Can not be determined
ব্যাখ্যা

Let,
Fahim's age = x
Bilash's age = y and
Wasim's age = z.

According to the given information
Age of Bilash - Age of Fahim = Age of Fahim - Age of Wasim
⇒ y - x = x - z
⇒ 2x = y + z ......(i)
Also, y + z = 66
from (i) x = 33 years

but, y + z = 66 means, there can be many sets of values that will satisfy the equation.
01 - 65
02 - 64
... ... ...
32 - 34

We want to determine x - z but as we can't get a fixed value for z; hence, the answer can not be determined.

৩০৩.
Six years ago, the ratio of the ages of Sahin and Robin was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Robin’s age at present?
  1. ক
    12 years
  2. খ
    14 years
  3. গ
    16 years
  4. ঘ
    18 years
ব্যাখ্যা
Question: Six years ago, the ratio of the ages of Sahin and Robin was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Robin’s age at present?

Solution:
Let, the ages of Shahin 6 years ago be = 6a years
And the ages of Robin 6 years ago be = 5a years respectively

Then, {(6a + 6) + 4}/{(5a + 6) + 4} = 11/10
⇒ 10{(6a + 6) + 4} = 11(5a + 6) + 4}
⇒ 10(6a + 10) = 11(5a + 10)
⇒ 60a + 100 = 55a + 110
⇒ 60a - 55a = 110 - 100
⇒ 5a = 10
∴ a = 2

∴ Robin’s present age = (5a + 6) = 16 years
৩০৪.
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 37, then how old is B?
  1. ক
    5 years
  2. খ
    7 years
  3. গ
    22 years
  4. ঘ
    14 years
ব্যাখ্যা
Question: A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 37, then how old is B?
 
Solution:
Let, C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years.
 
According to the question,
(2x + 2) + 2x + x = 37
⇒ 5x = 37 - 2
⇒ 5x = 35
∴ x = 7
 
Hence, B's age = 2x = 14 years.
৩০৫.
The present ages of three cousins are in the ratio of 4 : 5 : 6. Five years ago, their total age was 60 years. In three years, what will be the age of the youngest cousin?
  1. ক
    19 years
  2. খ
    23 years
  3. গ
    25 years
  4. ঘ
    28 years
ব্যাখ্যা

Question: The present ages of three cousins are in the ratio of 4 : 5 : 6. Five years ago, their total age was 60 years. In three years, what will be the age of the youngest cousin?

Solution: Present age ratio of three cousins is 4 : 5 : 6
Let, their age is 4X, 5X and 6X respectively.

ATQ,
4X - 5 + 5X - 5 + 6X - 5 = 60
Or, 15X - 15 = 60
Or, 15X = 75
Or, X = 5

∴ The present age of the youngest cousin is = 4X = 4 × 5 = 20 years.
In three years, his age will be = (20 + 3) = 23 years.

৩০৬.
The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:
  1. ক
    35 years
  2. খ
    40 years
  3. গ
    45 years
  4. ঘ
    50 years
ব্যাখ্যা
Question: The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband is:

Solution:
Sum of the present ages of husband, wife and child =(27 × 3 + 3 × 3) years
= (81 + 9) years
= 90 years

Sum of the present ages of wife and child =(20 × 2 + 5 × 2) years 
= (40 + 10) years 
= 50 years 

∴ Husband's present age =(90 - 50) years = 40 years.
৩০৭.
In a group of five men, no two men have the same age. The oldest man is 50 years old, and the youngest is 30 years old. If X is the average age of the men in the group, which of the following best indicates all and only possible values of X? (All ages are in whole numbers)
  1. ক
    30 < X < 50
  2. খ
    31 < X < 49
  3. গ
    32 < X < 48
  4. ঘ
    35 < X < 45
ব্যাখ্যা

Question: In a group of five men, no two men have the same age. The oldest man is 50 years old, and the youngest is 30 years old. If X is the average age of the men in the group, which of the following best indicates all and only possible values of X? (All ages are in whole numbers)

Solution: 
Here, 
Oldest man = 50 years
Youngest man = 30 years
Average age = X

Since no two people are the same age, the minimum average = (30 + 31 + 32 + 33 + 50)/5
= 176/5
= 35.2 
and the maximum average = (30 + 47 + 48 + 49 + 50)/5
= 224/5
= 44.8

That is, the value of X is greater than 35 and less than 45.
i.e. 35 < X < 45 

৩০৮.
The ratio of the present ages of Tina and Bina is 9 : 10 respectively. Twenty years ago, the ratio of their ages was 4 : 5 respectively. What is the present age of Bina?
  1. ক
    ক) 30 years
  2. খ
    খ) 35 years
  3. গ
    গ) 40 years
  4. ঘ
    ঘ) 42 years
ব্যাখ্যা
Ratio of the present ages of Tina and Bina = 9 : 10
Let's consider the present ages of Tina and Bina as 9x and 10x

According to the question 
(9x - 20) : (10x - 20) = 4 : 5
(9x - 20) / (10x - 20) = 4/5
5(9x - 20) = 4(10x - 20)
45x - 100 = 40x - 80
45x - 40x = 100 - 80
5x = 20
x = 4 

the present age of Bina = 40 years
৩০৯.
Eight years back, Adil's age was 1/8th of Zaher's age. Ten years from now, Zaher's age will be double of Adil's age. How many years old is Adil now?
  1. ক
    ক) 23
  2. খ
    খ) 21
  3. গ
    গ) 17
  4. ঘ
    ঘ) 11
ব্যাখ্যা
প্রশ্ন: Eight years back, Adil's age was 1/8th of Zaher's age. Ten years from now, Zaher's age will be double of Adil's age. How many years old is Adil now?

সমাধান: 
ধরি,
জহিরের বর্তমান বয়স ক বছর
৮ বছর পূর্বে জহিরের বয়স ক - ৮ বছর 
∴ ৮ বছর পূর্বে আদিলের বয়স (ক - ৮)/৮ বছর 

বর্তমানে,
আদিলের বয়স = (ক - ৮)/৮ + ৮ বছর 
= (ক - ৮ + ৬৪)/৮ বছর 
= (ক + ৫৬)/৮ বছর 

১০ বছর পর জহিরের বয়স হবে ক + ১০ বছর 
১০ বছর পর আদিলের বয়স হবে (ক + ৫৬)/৮ + ১০ বছর 
= (ক + ৫৬ + ৮০)/৮ বছর 
= (ক + ১৩৬)/৮ বছর 

প্রশ্নমতে, 
ক + ১০ = ২ ×{(ক + ১৩৬)/৮}
বা, ক + ১০ = (ক + ১৩৬)/৪  
বা, ৪(ক + ১০) = ক + ১৩৬
বা, ৪ক + ৪০  = ক + ১৩৬
বা, ৪ক - ক = ১৩৬ - ৪০
বা, ৩ক = ৯৬
বা, ক = ৯৬/৩
∴ ক = ৩২

∴ আদিলের বর্তমান বয়স = ( ৩২ + ৫৬)/৮ বছর 
= ৮৮/৮ বছর 
= ১১ বছর 
৩১০.
Didar is younger to Rohan by 9 years. If their ages are in the respective ratio of 4 : 5, how old is Didar?
  1. ক
    36 years
  2. খ
    23 years
  3. গ
    29 years
  4. ঘ
    Cannot be determined
  5. ঙ
    None of these
ব্যাখ্যা
Question: Didar is younger to Rohan by 9 years. If their ages are in the respective ratio of 4 : 5, how old is Didar?

Solution:
Let Rohan's age be x years.
Then,
Didar's age = (x - 9) years.

(x - 9)/x = 4/5
⇒ 5x - 45 = 4x
∴ x = 45
Hence, Didar's age = (x - 9) = 45 - 9 = 36 years.
৩১১.
A mother was 27 years old when her daughter was born. Currently, the mother's age is 9 years more than three times her daughter's age. How old will the daughter be in 6 years?
  1. ক
    12
  2. খ
    15
  3. গ
    21
  4. ঘ
    18
ব্যাখ্যা

Question: A mother was 27 years old when her daughter was born. Currently, the mother's age is 9 years more than three times her daughter's age. How old will the daughter be in 6 years?

Solution:
Let the daughter's current age be x years.
∴ Mother's current age = 3x + 9 years.

According to the question,
3x + 9 - x = 27
⇒ 2x = 27 - 9
⇒ 2x = 18
∴ x  = 9

∴ Daughter's current age 9 years.
∴ Daughter's age after 6 years = 9 + 6 = 15 years.

৩১২.
At present, the ratio between the ages of Haseena and Anushka is 4 : 3. After 6 years, Haseena's age will be 26 years. What is the present age of Anushka?
  1. ক
    15 years
  2. খ
    14 years
  3. গ
    13 years
  4. ঘ
    12 years
ব্যাখ্যা
Question: At present, the ratio between the ages of Haseena and Anushka is 4 : 3. After 6 years, Haseena's age will be 26 years. What is the present age of Anushka?

Solution:
After 6 years, Haseena's age will be 26 years
Therefore, the Present age of Haseena = 26 - 6 = 20
Let the present age of Anushka = x
Then,
20/x = 4/3
⇒ x = (20 × 3)/4
∴ x = 15 Years
৩১৩.
Four years ago a man was 6 times as old as his son. After 16 years he will be twice as old as his son. What is the present age of man and his son?
  1. ক
    34, 9
  2. খ
    33, 7
  3. গ
    35, 5
  4. ঘ
    36, 6
ব্যাখ্যা
Question: Four years ago a man was 6 times as old as his son. After 16 years he will be twice as old as his son. What is the present age of man and his son?

Solution:
Let age of son 4 years ago be = X
So, age of man 4 years ago would be = 6X

As per question after 16 years;
2 × age of son = age of man
2(X + 4 +16) = (6X + 4 + 16)
⇒ 2X + 40 = 6X + 20
⇒ 2X - 6X = 20 - 40
⇒ - 4X = - 20
∴ X = 5 years

∴ Present age of son = 5 + 4 = 9 years
∴ Present age of man = 6X + 4 = 6 × 5 + 4 = 30 + 4 = 34 years
৩১৪.
The present ages of A and B are in the ratio 6 : 4. Five years ago their ages were in the ratio 5 : 3. Find their present ages.
  1. ক
    ক) 42, 28
  2. খ
    খ) 36. 24
  3. গ
    গ) 30, 20
  4. ঘ
    ঘ) 25, 15
  5. ঙ
    ঙ) None of these
ব্যাখ্যা
Question: The present ages of A and B are in the ratio 6 : 4. Five years ago their ages were in the ratio 5: 3. Find their present ages.

Solution: 
বর্তমানে A এর বয়স 6x বছর 
বর্তমানে B এর বয়স 4x বছর

5 বছর আগে, A এর বয়স 6x - 5 বছর 
5 বছর আগে, B এর বয়স 4x - 5 বছর 

প্রশ্নমতে, 
(6x - 5)/(4x - 5) = 5/3
⇒ 18x - 15 = 20x - 25 
⇒ 20x - 18x = 25 - 15
⇒ 2x = 10
⇒ x = 5

বর্তমানে A এর বয়স = (6 × 5) = 30 বছর 
বর্তমানে B এর বয়স = (4 × 5) বছর = 20 বছর 
৩১৫.
The ratio of Sara’s age 4 years ago and Vaishali’s age after 4 years is 1 : 1. Presently, the ratio of their ages is 5 : 3. Find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.
  1. ক
    1 : 3
  2. খ
    3 : 1
  3. গ
    4 : 3
  4. ঘ
    3 : 4
  5. ঙ
    None of these
ব্যাখ্যা
Question: The ratio of Sara’s age 4 years ago and Vaishali’s age after 4 years is 1 : 1. Presently, the ratio of their ages is 5 : 3. Find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.

Solution:
Currently, the ratio of their ages is 5 : 3. Suppose, their ages are: 5x and 3x.
Sara’s age 4 years ago = 5x -  4
Vaishali’s age after 4 years = 3x + 4
Ratio of Sara’s age 4 years ago and Vaishali's age after 4 years is 1 : 1
Therefore,
(5x - 4)/(3x + 4) = 1/1
⇒ 5x - 4 = 3x + 4
⇒ 2x = 8
∴ x = 4
We are required to find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.
Sara's age: (5x + 4)
Vaishali's age: (3x - 4)
Putting the value of x, we get:
(5x + 4)/(3x - 4) = 24/8 = 3/1 = 3 : 1
৩১৬.
The present ages of John and Mary are In the ratio of 6 : 4. Five years ago their ages were in the ratio of 5 : 3. How old is John now?
  1. ক
    ক) 42
  2. খ
    খ) 36
  3. গ
    গ) 30
  4. ঘ
    ঘ) 24
ব্যাখ্যা

ATQ,
6x - 5 : 4x - 5 = 5 : 3
Or, 20x - 25 = 18x - 15
Or, 2x = 10
Or, x = 5
So, John's age now is = 6×5 = 30 years

৩১৭.
A is five times as old as B. 5 years ago, A was ten times as old as B. What will be the sum of their ages after 8 years?
  1. ক
    65 years
  2. খ
    70 years
  3. গ
    93 years
  4. ঘ
    84 years
ব্যাখ্যা

Question: A is five times as old as B. 5 years ago, A was ten times as old as B. What will be the sum of their ages after 8 years?

সমাধান:
ধরি,
B-এর বর্তমান বয়স = x বছর
A-এর বর্তমান বয়স = 5x বছর

5 বছর আগে,
B-এর বয়স ছিল = (x - 5) বছর
A-এর বয়স ছিল = (5x - 5) বছর

প্রশ্নমতে,
5x - 5 = 10(x - 5)
⇒ 5x - 5 = 10x - 50
⇒ 50 - 5 = 10x - 5x
⇒ 45 = 5x
⇒ x = 45/5
∴ x = 9

সুতরাং, B-এর বর্তমান বয়স 9 বছর এবং A-এর বর্তমান বয়স 5 × 9 = 45 বছর।

8 বছর পর,
B-এর বয়স হবে = 9 + 8 = 17 বছর
A-এর বয়স হবে = 45 + 8 = 53 বছর

∴ 8 বছর পর তাদের বয়সের সমষ্টি হবে = 17 + 53 = 70 বছর।

৩১৮.
The sum of ages of 5 children born at the intervals of 4 years each is 60 years. What is the age of the third oldest among them?
  1. ক
    3 years
  2. খ
    8 years
  3. গ
    10 years
  4. ঘ
    12 years
ব্যাখ্যা
Question: The sum of ages of 5 children born at the intervals of 4 years each is 60 years. What is the age of the third oldest among them?

Solution:
ধরি,
ছোট সন্তানের বয়স = ক বছর

প্রশ্নমতে,
ক + (ক + 4) + (ক + 8) + (ক + 12) + (ক + 16) = 60
⇒ 5ক + 40 = 60
⇒ 5ক = 60 - 40
⇒ 5ক = 20
⇒ ক = 20/5
⇒ ক = 4

অর্থাৎ ছোট সন্তানের বয়স = 4 বছর 
∴ তৃতীয় সন্তানের বয়স = (4 + 8) বছর = 12 বছর
৩১৯.
The sum of present ages of a father and his son is 8 years more than the present age of the mother. The mother is 22 years older than the son. What will be the age of the father after 4 years?
  1. ক
    34 years
  2. খ
    36 years
  3. গ
    40 years
  4. ঘ
    38 years
ব্যাখ্যা
Question: The sum of present ages of a father and his son is 8 years more than the present age of the mother. The mother is 22 years older than the son. What will be the age of the father after 4 years?

Solution:
Let present age of father, mother and son be x, y and z respectively
Sum of present ages of father and son = (Mother's present age + 8 years)
x + z = y + 8 years.................(i)

Mother's present age = Son's present age + 22 years
⇒ y = z + 22 years..............(ii)

Put the value of y in equation (i) we get
x + z = z + 22 + 8
x + z = z + 30
x = 30 years

∴ Father's present age = 30 years
Age of father after four years = 30 + 4 = 34 years
∴ Required age of father = 34 years
৩২০.
The average age of parents is 38 years. The average age of parents and a child is 30 years. What is the age is the child?
  1. ক
    ক) 10 years
  2. খ
    খ) 12 years
  3. গ
    গ) 14 years
  4. ঘ
    ঘ) 15 years
ব্যাখ্যা
Question: The average age of parents is 38 years. The average age of parents and a child is 30 years. What is the age is the child?

Solution:
Total age of parents = 38 × 2 = 76 years
Total age of parents and the child = 30 × 3 = 90 years

So, Child's age = 90 - 76 = 14 years
৩২১.
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother, what is the present age of the person?
  1. ক
    40 years
  2. খ
    25 years
  3. গ
    16 years
  4. ঘ
    8 years
ব্যাখ্যা
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother, what is the present age of the person?

Solution: 
Let,
The present age of the person’s mother be x years
∴ Age of the person is = (2x)/5 years

After 8 years,
Age of the person’s mother will be = x + 8 years
Age of the person will be = (2x)/5 + 8 years

ATQ,
(2x)/5 + 8 = (x + 8)/2
⇒ (2x)/5 + 8 = (x/2) + 4
⇒ (x/2) -  (2x)/5 = 8 - 4
⇒ (5x - 4x)/10 = 4
⇒ x/10 = 4
∴ x = 40

So, the present age of the person is  (2 × 40)/5 = 80/5 = 16 years
৩২২.
Jony got married 8 years ago. Today his age is 9/7 times his age at the time of his marriage. At present his daughter's age is one-sixth of his age. What was his daughter's age 3 years ago?
  1. ক
    3 years
  2. খ
    4 years
  3. গ
    6 years
  4. ঘ
    9 years
ব্যাখ্যা
Question: Jony got married 8 years ago. Today his age is 9/7 times his age at the time of his marriage. At present his daughter's age is one-sixth of his age. What was his daughter's age 3 years ago?

Solution:
Let, Jony's age 8 years ago be x years.
Then, his present age (x + 8) years.

ATQ,
x + 8 = 9x/7
⇒ 9x = 7x + 56
⇒ 9x - 7x = 56
⇒ 2x = 56
∴ x = 28

Jony's age now = x + 8 = 28 + 8 = 36 years.
His daughter's age now = 36/6 = 6 years.
His daughter's age 3 years ago = (6 - 3) = 3 years.
৩২৩.
A woman says, ''If you reverse my own age, the figures represent my husband's age. He is, of course, senior to me and the difference between our ages is one-eleventh of their sum.'' The woman's age is
  1. ক
    ক) 23 years
  2. খ
    খ) 34 years
  3. গ
    গ) 45 years
  4. ঘ
    ঘ) 54 years
ব্যাখ্যা

Let x and y be the ten's and unit's digits respectively of the numeral denoting the woman's age.

Then, woman's age = (10X + y) years;
husband's age = (10y + x) years.
Therefore (10y + x) - (10X + y) = (1/11) (10y + x + 10x + y)
⇒ (9y - 9x) = (1/11)(11y + 11x) = (x + y)
⇒ 10x = 8y
⇒ x = (4/5)y

Clearly, y should be a single-digit multiple of 5, which is 5.
So, x = 4, y = 5.
Hence, woman's age = 10x + y = 45 years.

৩২৪.
The present age of a father is five times that of his son. Eight years from now, the son's age will equal one-third of the father's age at that time. How old will the father be in 2 years?
  1. ক
    40 years
  2. খ
    42 years
  3. গ
    50 years
  4. ঘ
    48 years
ব্যাখ্যা
Question: The present age of a father is five times that of his son. Eight years from now, the son's age will equal one-third of the father's age at that time. How old will the father be in 2 years?

Solution:
ধরি,
পুত্রের বর্তমান বয়স = x বছর
পিতার বর্তমান বয়স = 5x বছর 

8 বছর পর,
পুত্রের বয়স হবে = (x + 8) বছর 
পিতার বয়স হবে = (5x + 8) বছর 

প্রশ্নমতে,
(x + 8) = (1/3) × (5x + 8)
3(x + 8) = 5x + 8
3x + 24 = 5x + 8
5x - 3x = 24 - 8
2x = 16
x = 16/2
x = 8

∴ পুত্রের বর্তমান বয়স = 8 বছর 
এবং পিতার বর্তমান বয়স = (5 × 8) বছর = 40 বছর

∴ 2 বছর পর পিতার বয়স হবে = (40 + 2) বছর = 42 বছর 
৩২৫.
The ratio of the ages of father and son now is 6 : 1. After 5 years the ratio will become 7 : 2. What is the sum of their ages now?
  1. ক
    ক) 35 years
  2. খ
    খ) 30 years
  3. গ
    গ) 40 years
  4. ঘ
    ঘ) 45 years
ব্যাখ্যা
Question: The ratio of the ages of father and son now is 6 : 1. After 5 years the ratio will become 7 : 2. What is the sum of their ages now?

Solution:
Let, the ages of the father = 6x
and the ages of the son = x

ATQ,
(6x + 5) / (x +5) = 7/2
⇒ 12x + 10 = 7x + 35
⇒ 5x = 25
⇒ x = 5

So, the ages of the son = 5 years
and the ages of the father = 6 × 5 = 30 years

∴ the sum of their ages now = 30 + 5 = 35 years
৩২৬.
Ten years ago, A was half of B in age. If the ratio of their present ages is 3 : 4, then what will be the total of their present ages?
  1. ক
    30 years
  2. খ
    35 years
  3. গ
    40 years
  4. ঘ
    45 years
ব্যাখ্যা
Let, present age of A = 3y
and present age of B = 4y
10 years ago, age of A = 3y - 10
10 years ago, age of B = 4y - 10
10 years ago, A = B/2
Therefore, 3y - 10 = (4y - 10)/2
or, y = 5
sum of age of A and B =3y + 4y = 7y = 35 years
৩২৭.
The average age of family of 6 members is 30 years. A new member is added then the average age becomes 26 years. Find the age of the new member.
  1. ক
    2 years
  2. খ
    5 years
  3. গ
    6 years
  4. ঘ
    11 years
ব্যাখ্যা
Question: The average age of family of 6 members is 30 years. A new member is added then the average age becomes 26 years. Find the age of the new member.

Solution:
Total age of 6 family members = (6 × 30) = 180 years

Total age of 7 members (after adding the new one) = (7 × 26) = 182 years

∴ Age of the new member = (182 - 180) = 2 years

The new member is 2 years old.
৩২৮.
Present age of Husband and Wife is 28 and 24 Years respectively. At that age twin babies were born to them. After how many years the average of the family will be same as before babies were born?
  1. ক
    11
  2. খ
    13
  3. গ
    15
  4. ঘ
    17
  5. ঙ
    19
ব্যাখ্যা

Total Age = 28 + 24 = 52
Average Age = 52/2
= 26

Let,
After T years their age will be the same as before.
ATQ,
24 + T + 28 + T + T + T = 26 × 4 = 104
Or, 4T = 52
Or, T = 52/4
Or, T = 13 years

So after 13 years their age will be the same average as before.

৩২৯.
Ten years ago, the age of mother was three times the age of her son. After ten years, mother’s age will be twice that of his son. Find the ratio of their present ages.
  1. ক
    7 : 3
  2. খ
    7 : 4
  3. গ
    9 : 5
  4. ঘ
    11 : 7
  5. ঙ
    None of these
ব্যাখ্যা
Question: Ten years ago, the age of mother was three times the age of her son. After ten years, mother’s age will be twice that of his son. Find the ratio of their present ages.

Solution:
10 years ago, age of mother was three times the age of her son.
Say, the age of son was x and mother's age was 3x.
At present:
Mother's age is (3x + 10)
and son’s age is (x + 10)

After ten years:
Mother's age will be (3x + 10) +10
and son’s age will be (x + 10) + 10.

Given that, mother’s age is twice that of son after ten years.
(3x + 10) +10 = 2 [(x + 10) + 10]
(3x + 20) = 2[x + 20]
Solving the equation, we get x = 20
(3x + 10) : (x + 10) = 70 : 30 = 7 : 3.
৩৩০.
A father said to his son, 'I was as old as you are at the present at the time of your birth'. If the father's age is 48 years now, the son's age three years back was-
  1. ক
    ক) 24 years
  2. খ
    খ) 21 years
  3. গ
    গ) 22 years
  4. ঘ
    ঘ) 23 years
ব্যাখ্যা
Question: A father said to his son, 'I was as old as you are at the present at the time of your birth'. If the father's age is 48 years now, the son's age three years back was-

Solution:
let, at present son is x years old
so, at time of his birth the father was x years old

∴ at present the age of father is = x + x year
= 2x year

2x = 48
⇒ x = 48/2
= 24 year

∴ the son's age five years back was = 24 - 3
= 21 year
৩৩১.
The sum of present ages of a father and his son is 8 years more than the present age of the mother. The mother is 22 years older than the son. What is the present age of the father?
  1. ক
    ক) 30 years
  2. খ
    খ) 34 years
  3. গ
    গ) 40 years
  4. ঘ
    ঘ) 42 years
ব্যাখ্যা
Question: The sum of present ages of a father and his son is 8 years more than the present age of the mother. The mother is 22 years older than the son. What is the present age of the father?

Solution:
Let, the present age of son = x and father = y.
So, present age of mother = x + 22

ATQ,
(y + x) - (x + 22) = 8
⇒ y = 8 + 22
⇒ y = 30

So, the present age of the father is 30 years
৩৩২.
A person's present age is two-fifth of the age of his mother. After 8 years, he will be one half of the age of his mother. What is the present age of the mother?
  1. ক
    ক) 30
  2. খ
    খ) 35
  3. গ
    গ) 40
  4. ঘ
    ঘ) 50
ব্যাখ্যা
Question: A person's present age is two-fifth of the age of his mother. After 8 years, he will be one half of the age of his mother. What is the present age of the mother?

Solution: 
Let the age of the person’s mother be ‘x years
Age of the person = (2x/5)

After 8 years, age of the person’s mother = ‘x + 8’ years
Age of the person after 8 years = (2x/5) + 8 years

According to question:
(2x/5) + 8 = (1/2)(x + 8)
(2x/5) + 8 = (x/2) + 4
(x/2) -  (2x/5) = 8 - 4
(5x - 4x)/10 = 4
x/10 = 4
x = 40

So, the present age of his mother is 40 years
৩৩৩.
My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. if my sister was 4 years of age when my brother was born, then what was the age of my father and mother respectively when my brother was born?
  1. ক
    32 years, 29 years
  2. খ
    35 years, 33 years
  3. গ
    32 years, 23 years
  4. ঘ
    35 years, 29 years
ব্যাখ্যা
Question: My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. if my sister was 4 years of age when my brother was born, then what was the age of my father and mother respectively when my brother was born?

Solution: 
My Mother was 26 years of age when I was born
My brother is 3 years elder to me
Mother's age when my brother was born = 26 - 3 = 23 years 

My father was 28 years of age when my sister was born
my sister was 4 years of age when my brother was born
Father's age when my brother was born = 28 + 4 = 32 years 
৩৩৪.
A person's present age is two-fifth of the age of his mother. After 8 year, he will be one-half of the age of his mother. How old is the mother at present?
  1. ক
    ক) 36 years
  2. খ
    খ) 38 years
  3. গ
    গ) 40 years
  4. ঘ
    ঘ) 42 years
ব্যাখ্যা

Let the mother's present age be x year.
Then, the person's present age = 2/5 x year.
(2x/5 + 8) = 1/2 (x + 8)
2(2x + 40) = 5(x + 8) 
=> x = 40.

৩৩৫.
A man's present age is two-fifth of the ages of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present?
  1. ক
    ক) 36
  2. খ
    খ) 38
  3. গ
    গ) 40
  4. ঘ
    ঘ) 42
ব্যাখ্যা
Let present age of mother is x,
then present age of his son = 2x​/5

According to the question 
 (2x​/5) + 8 = (1/2)(x + 8)
(2x​/5) + 8 = x/2 + 4 
(2x​/5) - (x/2) = 4 - 8
(4x - 5x)/10 = - 4
- x/10 = - 4
x = 40

Hence, the present age of mother is 40
৩৩৬.
If 5 years ago, the ratio of age of Mredul and Tanni was 1 : 2 and after 15 years from present their ratio would be 5 : 6. Find the age of Tanni after 20 years.
  1. ক
    35 years
  2. খ
    30 years
  3. গ
    32 years
  4. ঘ
    28 years
ব্যাখ্যা
Question: If 5 years ago, the ratio of age of Mredul and Tanni was 1 : 2 and after 15 years from present their ratio would be 5 : 6. Find the age of Tanni after 20 years.

Solution:
Let, present age of Mredul be x and present age of Tanni be y.

Then, according to question (x - 5)/(y - 5) = 1/2
⇒ 2x - 10 = y - 5
⇒ x = (y + 5)/2 ............(1)

Also,
(x + 15)/(y + 15) = 5/6
⇒ 6x + 90 = 5y + 75
⇒ 6x + 15 = 5y

Putting value of x from equation (1), we get
6{(y + 5)/2} + 15 = 5y
⇒ 3y + 15 + 15 = 5y
⇒ 2y = 30
∴ y = 15

∴ Age of Tanni after 20 years = 15 + 20 = 35 years.
৩৩৭.
Mr. Babul is aged three times than his son Mahi. After 6 years, he would be two and a half times of Mahi's age. After further 6 years, how many times would he be of Mahi's age?
  1. ক
    3
  2. খ
    5/11
  3. গ
    11/5
  4. ঘ
    9/7
  5. ঙ
    7/9
ব্যাখ্যা

Question: Mr. Babul is aged three times than his son Mahi. After 6 years, he would be two and a half times of Mahi's age. After further 6 years, how many times would he be of Mahi's age?

Solution:
Let Mahi's present age be x years.
Then, Mr. Babul's present age = 3x years 

∴ After 6 years, Mahi's age will be (x + 6) years 
And, after 6 years, Mr. Babul's age will be (3x + 6) years

ATQ,
3x + 6 = (5/2) × (x + 6)
⇒ 3x + 6 = (5x + 30)/2  
⇒ 6x + 12 = 5x + 30
⇒ 6x - 5x = 30 - 12
⇒ x = 18

∴ After 6 years, Mahi's age will be (18 + 6) years
= 24 years
∴ After 6 years, Mr. Babul's age will be (3 × 18) + 6) years
= 54 + 6
= 60 years

∴ After further, 6 years, Mahi's age will be (24 + 6) years
= 30 years
∴ After 6 years, Mr. Babul's age will be (60 + 6) years
= 66 years

∴ Required Ratio = 66/30 
= 11/5 

∴ After further 6 years, Mr. Babul's age will be 11/5 times of Mahi's age.

৩৩৮.
If John was 27 years old 9 years ago, how old was he n years ago?
  1. ক
    ক) (36 - n) years
  2. খ
    খ) (35 - n) years
  3. গ
    গ) (36 + n) years
  4. ঘ
    ঘ) (18 - n) years
ব্যাখ্যা
John's present age = 27 + 9 = 36

n years ago, his age = (36 - n) years
৩৩৯.
If the total ages of Iqbal and Shikhar is 12 years more than the total age of Shikhar and Charu. Charu is how many years younger than Iqbal?
  1. ক
    11 years
  2. খ
    13 years
  3. গ
    15 years
  4. ঘ
    Cannot be Determined
  5. ঙ
    None of the above
ব্যাখ্যা
Question: If the total ages of Iqbal and Shikhar is 12 years more than the total age of Shikhar and Charu. Charu is how many years younger than Iqbal?

Solution:
Let the age of Iqbal be x
Let the age of Shikhar be y
Let the age of Charu be z
 
Then, according to question, 
(x + y) - (y + z) = 12
⇒ x + y - y - z = 12
⇒ x - z = 12
Thus, Charu is 12 years younger than Iqbal
৩৪০.
The average age of 8 members of a group is 36 years. The age of the eldest member is 43 years. If we exclude that eldest member from the group, then what will be the average age (in years) of the remaining members?
  1. ক
    ক) 25 years
  2. খ
    খ) 35 years
  3. গ
    গ) 45 years
  4. ঘ
    ঘ) 55 years
ব্যাখ্যা
Question: The average age of 8 members of a group is 36 years. The age of the eldest member is 43 years. If we exclude that eldest member from the group, then what will be the average age (in years) of the remaining members?

Solution:
Total age = (36 × 8)
= 288
After excluding the eldest member, total age = 288 - 43
= 245 year

∴Now the average age of remaining members = 245/7
= 35 years
৩৪১.
A father said to his son, 'I was as old as you are at the present at the time of your birth'. If the father's age is 48 years now, the son's age five years back was-
  1. ক
    ক) 14 year
  2. খ
    খ) 19 year
  3. গ
    গ) 24 year
  4. ঘ
    ঘ) 30 year
ব্যাখ্যা
Question: A father said to his son, 'I was as old as you are at the present at the time of your birth'. If the father's age is 48 years now, the son's age five years back was-

Solution:
let, at present son is x years old
so, at time of his birth the father was x years old

∴ at present the age of father is = x + x year
= 2x year

2x = 48
⇒ x = 48/2
= 24 year

∴ the son's age five years back was = 24 -5 
= 19 year
৩৪২.
Ten years ago. A was half of B in age. If the ratio of their present age is 3 : 4 What will be the total of their present ages?
  1. ক
    20 years
  2. খ
    30 years
  3. গ
    45 years
  4. ঘ
    None of these
ব্যাখ্যা
Question: Ten years ago. A was half of B in age. If the ratio of their present age is 3 : 4. What will be the total of their present ages?

Solution: 
let, Ten years ago, A was x years old
B was 2x years old 

ATQ, 
(x + 10)/(2x + 10) = 3/4
⇒ 4x + 40 = 6x = 30 
⇒ 6x - 4x = 40 - 30 
⇒ 2x = 10 
∴ x = 5 

total present age = x + 2x + 20 
= 3x + 20 
= 3 × 5 + 20 
= 35 years
৩৪৩.
Today is Ratul's 12th birthday and his father's 40th birthday. How many years form today will Ratul's father be twice as old as Ratul's at that time?
  1. ক
    16 years
  2. খ
    21 years
  3. গ
    20 years
  4. ঘ
    14 years
ব্যাখ্যা

Question: Today is Ratul's 12th birthday and his father's 40th birthday. How many years form today will Ratul's father be twice as old as Ratul's at that time?

Solution:
Given that,
Today Ratul is 12 years old
And his Father is 40 years old
Age difference = 40 - 12 = 28 years (constant)

Let After x years, father's age = 2 × Ratul's age

Now,
Ratul's age after x years = 12 + x
Father's age after x years = 40 + x

ATQ,
40 + x = 2 × (12 + x) 
⇒ 40 + x = 24 + 2x
⇒ x = 40 - 24
∴ x = 16

So, in 16 years, Ratul's father will be twice as old as Ratul.

৩৪৪.
পুত্র ও পিতার বর্তমান বয়সের অনুপাত 1 : 3। 3 বছর আগে তাদের বয়সের অনুপাত ছিল 2 : 7। 3 বছর পর তাদের বয়সের অনুপাত কত হবে?
  1. ক
    2 : 5
  2. খ
    4 : 8
  3. গ
    5 : 9
  4. ঘ
    3 : 8
  5. ঙ
    কোনটিই নয়
ব্যাখ্যা
প্রশ্ন: পুত্র ও পিতার বর্তমান বয়সের অনুপাত 1 : 3। 3 বছর আগে তাদের বয়সের অনুপাত ছিল 2 : 7। 3 বছর পর তাদের বয়সের অনুপাত কত হবে?

সমাধান:
ধরি,
পুত্রের বর্তমান বয়স = x বছর এবং
পিতার বর্তমান বয়স = 3x বছর

প্রশ্নমতে,
(x - 3)/(3x - 3) = 2/7
বা, 7x - 21 = 6x - 6
বা, 7x - 6x = 21 - 6
∴ x = 15

সুতরাং তাদের বর্তমান বয়স 15 বছর এবং = 3 × 15 = 45 বছর  
3 বছর পর তাদের বয়সের অনুপাত হবে (15 + 3): (45 + 3)
= 18 : 48
= 3 : 8
৩৪৫.
One year ago the ratio between Maruf and Hasan's age was 4 : 3. One year hence the ratio of their age will be 5 : 4. What is the sum of their present ages in years?
  1. ক
    14 years
  2. খ
    22 years
  3. গ
    20 years
  4. ঘ
    16 years
  5. ঙ
    None of these
ব্যাখ্যা
Question: One year ago the ratio between Maruf and Hasan's age was 4 : 3. One year hence the ratio of their age will be 5 : 4. What is the sum of their present ages in years?

Solution:
ধরি,
Maruf-এর বয়স ছিল = 4x
Hasan-এর বয়স ছিল = 3x

বর্তমানে,
Maruf-এর বয়স = 4x + 1
Hasan-এর বয়স = 3x + 1

আবার,
1 বছর পর, Maruf-এর বয়স = 4x + 1 + 1 = 4x + 2 বছর
Hasan-এর বয়স = 3x + 1 + 1 = 3x + 2 বছর

এখন,
⇒ 4x + 2 : 3x + 2 = 5 : 4
⇒ (4x + 2)/(3x + 2) = 5/4
⇒ 16x + 8 = 15x + 10
⇒ 16x - 15x = 10 - 8
∴ x = 2

বর্তমানে, Maruf-এর বয়স = 4 × 2 + 1 = 9 বছর
Hasan-এর বয়স = 3 × 2 + 1 = 7 বছর

∴ তাদের বয়সের যোগফাল = 9 + 7 = 16 বছর।
৩৪৬.
The present ages of Hasan and Kamal are in the ratio 4 : 5. After 6 years, the ratio of their ages will be 5 : 6. What is the difference in their present ages?
  1. ক
    12 years
  2. খ
    6 years
  3. গ
    10 years
  4. ঘ
    8 years
ব্যাখ্যা

Question: The present ages of Hasan and Kamal are in the ratio 4 : 5. After 6 years, the ratio of their ages will be 5 : 6. What is the difference in their present ages?

Solution:
Let, their present ages be 4x and 5x.

After 6 years,
Hasan's age = 4x + 6
Kamal's age = 5x + 6

According to the question,
(4x + 6)/(5x + 6) = 5/6
⇒ 6(4x + 6) = 5(5x + 6)
⇒ 24x + 36 = 25x + 30
⇒ 25x − 24x = 36 − 30
⇒ x = 6

Hasan's present age = 4 × 6 = 24 years
Kamal's present age = 5 × 6 = 30 years

∴ Difference = 30 − 24 = 6 years

৩৪৭.
The present age of son is half of the present age of his mother. Ten years ago, his mother's age was thrice the age of her son. What is the present age of the mother?
  1. ক
    ক) 40 years
  2. খ
    খ) 50 years
  3. গ
    গ) 60 years
  4. ঘ
    ঘ) 80 years
ব্যাখ্যা
Question: The present age of son is half of the present age of his mother. Ten years ago, his mother's age was thrice the age of her son. What is the present age of the mother?

Solution:
Let, the mother's age be = 2x years
Then, the son's age = x years

∴(2x − 10) = 3(x − 10)
⇒2x − 10 = 3x −30
⇒x = 20

Son's age = 20 years
Mother's age = (2 × 20) = 40 years
৩৪৮.
Mr. P has three daughters, S, M and T. Three years ago, when Mr. P was twice as old as T, he was 30 years older than M. Now he is 47 years older than S. In 4 years, S will be half as old as T. What is the age of S?
  1. ক
    12 years
  2. খ
    14 years
  3. গ
    16 years
  4. ঘ
    18 years
ব্যাখ্যা
Question: Mr. P has three daughters, S, M and T. Three years ago, when Mr. P was twice as old as T, he was 30 years older than M. Now he is 47 years older than S. In 4 years, S will be half as old as T. What is the age of S?

Solution:
ATQ,
K - 3 = 2(T - 3) .......... (1)
K = M + 30 ......... (2)
K = S + 47 ............ (3)
∴ 2(S + 4) = T + 4
⇒ 2s + 8 = T + 4
⇒ 2s + 8 - 4 = T
⇒ 2s + 4 = T
From (1) we get K - 3 = 2(2S + 4 - 3)
⇒ K - 3 = 4S + 2
⇒ K = 4S + 5

From (3) we get, 4S + 5 = S + 47
⇒ 4S - S = 47 - 5
⇒ 3S = 42
∴ S = 14
৩৪৯.
The total age of A and B is 12 years more than the total age of B and C. C is how many years younger than A?
  1. ক
    ক) 12 years
  2. খ
    খ) 13 years
  3. গ
    গ) 14 years
  4. ঘ
    ঘ) 15 years
ব্যাখ্যা
এখানে 
A + B - (B + C) = 12
A + B - B - C = 12
A - C = 12
৩৫০.
Currently, the age of P is twice the age of Q. After 6 years, P's age will be 3/2 times the age of Q. What is the present age of P?
  1. ক
    12 years
  2. খ
    18 years
  3. গ
    24 years
  4. ঘ
    8 years
  5. ঙ
    6 years
ব্যাখ্যা

Question: Currently, the age of P is twice the age of Q. After 6 years, P's age will be 3/2 times the age of Q. What is the present age of P?

Solution:
Let the present age of Q = x years
Then the present age of P = 2x years

After 6 years, age of P = 2x + 6
And age of Q = x + 6

According to the question,
After 6 years, P's age will be 3/2 times Q's age. So,
⇒ 2x + 6 = (3/2) × (x + 6)
⇒ 2(2x + 6) = 3(x + 6)
⇒ 4x + 12 = 3x + 18
⇒ 4x - 3x = 18 - 12
∴ x = 6
Therefore, Present age of Q = 6 years
And present age of P = 2x = 12 years.

So the present age of P is 12 years.

৩৫১.
The difference of ages between two brothers is 6 years. If the ratio of their ages is 7 : 5, find their ages.
  1. ক
    Elder 21, Younger 15
  2. খ
    Elder 28, Younger 22
  3. গ
    Elder 35, Younger 29
  4. ঘ
    Elder 14, Younger 8
ব্যাখ্যা

Question: The difference of ages between two brothers is 6 years. If the ratio of their ages is 7 : 5, find their ages

Solution:
Let
The ages of the two brothers be 7x and 5x. (elder : younger).
Difference of ages = 6 

Accordingly, 
7x - 5x = 6
⇒ 2x = 6  
⇒ x = 3.

∴ Elder = 7x = 7 × 3 = 21 
∴ Younger = 5x = 5 × 3 = 15

So Elder brother 21 years and younger brother 15 years.

৩৫২.
A person’s age is 3 times the age of his friend. The total of their ages is 64 years. How old is the person?
  1. ক
    16 years
  2. খ
    42 years
  3. গ
    48 years
  4. ঘ
    52 years
ব্যাখ্যা
Question: A person’s age is 3 times the age of his friend. The total of their ages is 64 years. How old is the person?

Solution:
A person’s age is 3 times the age of his friend.
The total of their ages is 64 years.

Let, the age of the friend be x
Let the age of the person be 4x
Total of their ages = x + 3x

ATQ,
x + 3x = 64
⇒ 4x = 64
∴ x = 16

∴ The age of the friend = 16,
The age of the person = 16 × 3 = 48 years.

∴ The age of the person and friend is 48 years.
৩৫৩.
The average age of a group of 10 students was 20 years. The average age increased by 2 years when two new students joined the group. What is the average age of the two new students who joined the group?
  1. ক
    ক) 29 years
  2. খ
    খ) 30 years
  3. গ
    গ) 31 years
  4. ঘ
    ঘ) 32 years
ব্যাখ্যা
The average age of a group of 10 students was 20
Therefore, the total age of a group of 10 students was 20 × 10 = 200

The average age increased by 2 years when two new students joined the group.
That means, the average age of a group of (10 + 2) students was (20 + 2) years 
Therefore, the total age of a group of 12 students was 22 × 12 = 264 years

the total age of 2 students is (264 - 200) = 64 years 
The average age is 64/2 = 32 years 
-------------------------------------------------------------------------------
১০ জন ছাত্রের গড় বয়স ২০ বছর। নতুন ২ জন ছাত্র যোগ দিলে গড় বয়স ২ বছর বৃদ্ধি পায়। নতুন ২ জন ছাত্রের গড় বয়স কত?

১০ জন ছাত্রের গড় বয়স ২০ বছর। সুতরাং মোট বয়স = ২০ × ১০  = ২০০ বছর
নতুন ২ জন ছাত্র গ্রুপে যোগ দিলে গড় বয়স ২ বছর বৃদ্ধি পায়। 
সুতরাং (১০ + ২০) বা ১২ জন ছাত্রের গড় বয়স = (২০ + ২) বা ২২ বছর। সুতরাং মোট বয়স = ২২ × ১২ বা ২৬৪ বছর
অতএব ২ জন নতুন ছাত্রের মোট বয়স = ২৬৪ - ২০০ = ৬৪ বছর। অতএব গড় বয়স = ৬৪/২ = ৩২ বছর
৩৫৪.
Present age of Farid is thrice the present age of Sami who is 20. How many years ago was the age of Farid five times that of Sami?
  1. ক
    3
  2. খ
    6
  3. গ
    7.5
  4. ঘ
    10
ব্যাখ্যা
Question: Present age of Farid is thrice the present age of Sami who is 20. How many years ago was the age of Farid five times that of Sami?
 
Solution:
সামির বর্তমান বয়স ২০ বছর
∴ ফরিদের বর্তমান বয়স ২০× ৩ বছর 
= ৬০ বছর 
 
ধরি,
ক বছর আগে ফরিদের বয়স সামির বয়সের ৫ গুণ ছিল।
 
শর্তমতে,
৬০ - ক = ৫(২০ - ক)
বা, ৬০ - ক = ১০০ - ৫ক 
বা, ৪ক = ৪০ 
বা, ক = ৪০/৪ 
∴ ক = ১০
 
∴ ১০ বছর আগে ফরিদের বয়স সামির বয়সের ৫ গুণ ছিল।
৩৫৫.
Fahim is younger than Tanim by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Fahim?
  1. ক
    31 years
  2. খ
    31.5 years
  3. গ
    32 years
  4. ঘ
    24.5 years
ব্যাখ্যা
Question: Fahim is younger than Tanim by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Fahim?

Solution:
Let Tanim's age be x years.
Then, Fahim's age = (x - 7) years.

 ATQ,
(x - 7)/x = 7/9
⇒ 9((x - 7) = 7x
⇒ 9x - 63 = 7x
⇒ 9x - 7x = 63
⇒ 2x = 63
∴ x = 31.5

Fahim's age is (31.5 - 7) = 24.5 years.
৩৫৬.
The father's age is five times his son's age. Five years after, the age of the father will be three times his son's age. The present ages, in years, of the son and the father are respectively
  1. ক
    ক) 10 and 30
  2. খ
    খ) 5 and 25
  3. গ
    গ) 15 and 75
  4. ঘ
    ঘ) 18 and 54
  5. ঙ
    ঙ) None of these
ব্যাখ্যা
Question: The father's age is five times his son's age. Five years after, the age of the father will be three times his son's age. The present ages, in years, of the son and the father are respectively-

Solution:
মনে করি,
পুত্রের বর্তমান  বয়স = x বছর
এবং পিতার বর্তমান  বয়স = 5x বছর

প্রশ্নমতে,
5x + 5 = 3(x + 5)
⇒ 5x + 5 = 3x + 15 
⇒ 2x = 10
⇒  x = 5

পুত্রের বর্তমান  বয়স = 5 বছর
পিতার বর্তমান  বয়স = 5 × 5 = 25 বছর
৩৫৭.
A is twice as old as B. 12 years ago, A was five times as old as B. Find the present age of A.
  1. ক
    32 years
  2. খ
    36 years
  3. গ
    28 years
  4. ঘ
    42 years
ব্যাখ্যা

Question: A is twice as old as B. 12 years ago, A was five times as old as B. Find the present age of A.

Solution:
Let the present age of B is = x years.
Then the present age of A is = 2x years (since A is twice as old as B).

12 years ago,
Age of A = 2x - 12
and age of B = x - 12

According to the problem,
2x - 12 = 5(x - 12)
⇒ 2x - 12 = 5x - 60
⇒ 5x - 2x = - 12 + 60 
⇒ 3x = 48
⇒ x = 48/3
∴ x = 16

∴ Present age of B = 16 years
∴ Present age of A = 2 × 16 = 32 years

৩৫৮.
The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?
  1. ক
    12 years
  2. খ
    22 years
  3. গ
    6 years
  4. ঘ
    4 years
ব্যাখ্যা
Question: The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child?

Solution:
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
⇒ 5x + 30 = 50
⇒ 5x = 50 - 30 
⇒ 5x = 20
⇒ x = 4

∴ Age of the youngest child = x = 4 years.
৩৫৯.
The ages of Sabiha and Suriya are in the ratio of 7 : 3 respectively. After 6 years, the ratio of their ages will be 5 : 3. What is the difference in their ages?
  1. ক
    6 years
  2. খ
    8 years
  3. গ
    10 years
  4. ঘ
    12 years
ব্যাখ্যা
Question: The ages of Sabiha and Suriya are in the ratio of 7 : 3 respectively. After 6 years, the ratio of their ages will be 5 : 3. What is the difference in their ages?

Solution:
Let, their ages are 7x, 3x 

ATQ, 
(7x + 6)/(3x + 6) = 5/3
⇒ 3(7x + 6) = 5(3x + 6)
⇒ 21x + 18 = 15x + 30 
⇒ 21x - 15x = 30 - 18 
⇒ 6x = 12 
∴ x = 2 

 The difference in their ages is = 7x - 3x 
= 4x
= 4 × 2
= 8 years
৩৬০.
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
  1. ক
    8 years
  2. খ
    9 years
  3. গ
    10 years
  4. ঘ
    11 years
  5. ঙ
    14 years
ব্যাখ্যা
Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years. 
∴ (2x + 2) + 2x + x = 27
⇒ 5x = 25
⇒ x = 5.
Hence, B's age = 2x = 10 years.
৩৬১.
The difference between the present ages of Arun and Ashok is 12 years. Seven years ago, the ratio of their ages was 6 : 8 respectively. What is the Ashok's present age?
  1. ক
    45 years
  2. খ
    32 years
  3. গ
    53 years
  4. ঘ
    55 years
ব্যাখ্যা
Question: The difference between the present ages of Arun and Ashok is 12 years. Seven years ago, the ratio of their ages was 6 : 8 respectively. What is the Ashok's present age?

Solution:
Let, 7 years ago
Arun's age was 6x and Ashok's age was 8x

At present,
Arun's age is (6x + 7) years and Ashok's age is (8x + 7) years

According to the question,
⇒ (8x + 7) - (6x + 7) = 12
⇒ 8x + 7 - 6x - 7 = 12
⇒ 2x = 12
⇒ x = 12/2
⇒ x = 6

∴ Ashok's present age = 8x + 7 = 8 × 6 + 7 = 55 years
৩৬২.
Ten years ago, the age of a father was four times his son's age. Ten years from now, the father will be twice as old as his son. What is the ratio of their current ages?
  1. ক
    3 : 1
  2. খ
    5 : 2
  3. গ
    7 : 3
  4. ঘ
    9 : 4
ব্যাখ্যা
Question: Ten years ago, the age of a father was four times his son's age. Ten years from now, the father will be twice as old as his son. What is the ratio of their current ages?

Solution:
Let father’s current age = F,
son’s current age = S
Ten years ago:
F−10=4(S - 10)  
⟹  F−10=4S - 40 
 ⟹  F=4S - 30 ------------(Equation 1)

Ten years later:
F+10=2(S+10)  
⟹  F+10=2S+20  
⟹  F=2S+10 ------------(Equation 2)

Set Equation 1 = Equation 2 (উভয় এই পিতার বয়স):
4S−30=2S+10  ⟹  2S=40 
 ⟹  S=20

Then, F=2(20)+10=50
Ratio:
F : S
=50 : 20 =5 : 2
Answer: 5 : 2
৩৬৩.
Tania's grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. Eight years ago, what was the ratio of Tanya's age to that of her grandfather?
  1. ক
    ক) 1 : 2
  2. খ
    খ) 1 : 5
  3. গ
    গ) 2 : 3
  4. ঘ
    ঘ) 11 : 53
ব্যাখ্যা

16 years ago,
Let, Tania (T) = x years and Grandfather (G) = 8x years.
After 8 years from now,
T = (x + 16 + 8) years and G = (8x + 16 + 8) years.

8x + 24 = 3(x + 24)
⇒ 5x = 48
8 years ago,
T/G = (x + 8)/(8x + 8)
= {(48/5) + 8}/{8 × (48/5) + 8}
= (88/5)/(424/5)
= 88/424
= 11/53

৩৬৪.
৫ বছর পূর্বে পিতা পুত্রের বয়সের অনুপাত ছিল ৩ : ১ আর ১৫ বছর পরে পিতা পুত্রের বয়সের অনুপাত হবে ২ : ১। পিতা ও পুত্রের বর্তমান বয়স কত?
  1. ক
    ক) ৭৫, ২৫
  2. খ
    খ) ৬০, ২০
  3. গ
    গ) ৬৫, ২৫
  4. ঘ
    ঘ) ৩০, ৭০
ব্যাখ্যা
প্রশ্ন: ৫ বছর পূর্বে পিতা পুত্রের বয়সের অনুপাত ছিল ৩ : ১ আর ১৫ বছর পরে পিতা পুত্রের বয়সের অনুপাত হবে ২ : ১। পিতা ও পুত্রের বর্তমান বয়স কত? 

সমাধান: 
ধরি,
পিতার বর্তমান বয়স ক বছর 
পুত্রের বর্তমান বয়স খ বছর 

শর্তমতে,
(ক - ৫) : (খ - ৫) = ৩ : ১ 
বা, (ক - ৫)/(খ - ৫) = ৩/১
বা, ক - ৫ = ৩(খ - ৫)
বা, ক - ৫ = ৩খ - ১৫
∴ ক = ৩খ - ১০  ...................................(1)

আবার শর্তমতে,
(ক + ১৫) : (খ + ১৫) = ২ : ১
বা, (ক + ১৫)/(খ + ১৫) = ২/১
বা, ক + ১৫ = ২(খ + ১৫)
বা, ক + ১৫ = ২খ + ৩০
বা, ক = ২খ + ১৫  .................................(2)

(1) ও (2) নং থেকে পাই,
৩খ - ১০ = ২খ + ১৫
বা, খ = ২৫ 

খ এর মান (2) নং এ বসিয়ে পাই, 
ক = ২ × ২৫ + ১৫
বা, ক = ৫০ + ১৫ 
∴ ক = ৬৫

∴ পিতার বর্তমান বয়স ৬৫ বছর 
পুত্রের বর্তমান বয়স ২৫ বছর
৩৬৫.
Sum of the ages of 5 children born in regular intervals of 3 years each is 50 years. What is the age of the youngest children?
  1. ক
    ক) 4 years
  2. খ
    খ) 8 years
  3. গ
    গ) 10 years.
  4. ঘ
    ঘ) 6 years
  5. ঙ
    ঙ) None of these
ব্যাখ্যা

Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
⇒ 5x = 20
⇒ x = 4.
∴ Age of the youngest child = x = 4 years.

৩৬৬.
The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older than him. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team?
  1. ক
    ক) 23
  2. খ
    খ) 24
  3. গ
    গ) 25
  4. ঘ
    ঘ) None
ব্যাখ্যা

Given, Captain's age 26 years and Wicketkeeper's age 29 years.
Let, Average age be X years

ATQ,
9(x - 1) + 26 + 29 = 11x
⇒ 9x - 9 + 26 + 29 = 11x
⇒ 2x = 46
⇒ x = 23

৩৬৭.
The ages of Ram and Mohan are in the ratio of 5 : 7 and the difference between them is 12 years. The ages (in years) of Ram and Mohan are respectively:
  1. ক
    ক) 25 and 35 years
  2. খ
    খ) 20 and 28 years
  3. গ
    গ) 30 and 42 years
  4. ঘ
    ঘ) 28 and 40 years
ব্যাখ্যা
Let
the age of Ram and Mohan be 5x and 7x respectively
According to the question
⇒ 7x - 5x = 12
⇒ 2x = 12
⇒ x = 6

The age of Ram = 5 × 6 = 30 years
The age of Mohan = 7 × 6 = 42 years

∴ The required result will be "30 years and 42 years" respectively.
৩৬৮.
The average age of the 20 persons is 19.2 years. After some time two more persons join them and then average is increased by 0.3 years. Find the difference between the age of new persons.
  1. ক
    ক) 45 years
  2. খ
    খ) 32 years
  3. গ
    গ) 22 years
  4. ঘ
    ঘ) None of these
ব্যাখ্যা
The average age of the 20 persons is 19.2 years. Therefore, total age = 20 × 19.2 = 384 years 
After some time two more persons join them and then average is increased by 0.3 years.
So, average age of (20 + 2) or 22 persons = (19.2 + 0.3) years. Therefore, the total age = 22 × 19.5 = 429 years 
Total age of 2 new persons = 429 - 384) = 45 years 
It is possible to calculate to find the total age of two new persons but not difference.
--------------------------------------------------------------------------------------------------------------------
২০ জন ব্যক্তির গড় বয়স ১৯.২ বছর। কিছু দিন পর ২ জন নতুন ব্যক্তি যোগ দেওয়ায় গড় বয়স ০.৩ বছর বেড়ে গেলো। তাদের বয়সের বিয়োগফল কত?

২০ জন ব্যক্তির গড় বয়স ১৯.২ বছর হলে মোট বয়স ২০ × ১৯.২ = ৩৮৪ বছর
২ জন নতুন ব্যক্তি যোগ দেওয়ায় (২০ + ২) বা ২২ জনের গড় বয়স ০.৩ বছর বৃদ্ধি পেল। অতএব মোট বয়স = ২২ × (১৯.২ + ০.৩) = ২২ × ১৯.৫ = ৪২৯ বছর
২ জন নতুন ব্যক্তির মোট বয়স = ৪২৯ - ৩৮৪ = ৪৫ বছর 
২ জন নতুন ব্যক্তির মোট বয়স বের করা সম্ভব কিন্তু পর্যাপ্ত ডেটা না থাকায় তাদের বয়সের বিয়োগফল বের করা সম্ভব নয়।
৩৬৯.
A father is three times as old as his son. After fifteen years father will be twice as old as his son age that time. What is the present age of the son?
  1. ক
    ক) 10 years
  2. খ
    খ) 15 years
  3. গ
    গ) 20 years
  4. ঘ
    ঘ) 25 years
ব্যাখ্যা
Question: A father is three times as old as his son. After fifteen years father will be twice as old as his son age that time. What is the present age of the son?

Solution:
Let, the son's age be x years
and the father's age is = 3x years

ATQ,
3x + 15 = 2(x + 15)
⇒ 3x + 15 = 2x + 30
∴ x = 15

∴ Son's age 15 years.
৩৭০.
The ratio between the present ages of A and B is 3 : 5. If the ratio of their ages five years hence becomes 13 : 20, then the present age of B is:
  1. ক
    30 years
  2. খ
    33 years
  3. গ
    35 years
  4. ঘ
    37 years
ব্যাখ্যা
Question: The ratio between the present ages of A and B is 3 : 5. If the ratio of their ages five years hence becomes 13 : 20, then the present age of B is:

Solution:
Let's say A's present age is 3x and B's present age is 5x
After 5 years,
A's age will be = 3x + 5
B's age will be = 5x + 5

ATQ,
(3x + 5)/(5x + 5) = 13/20
⇒ 20(3x + 5) = 13(5x + 5)
⇒ 60x + 100 = 65x + 65
⇒ 60x - 65x = 65 - 100
⇒ - 5x = - 35
∴ x = 7

Since B's present age = 5x = 5 × 7 = 35 years
৩৭১.
The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).
  1. ক
    ক) 16, 24, 36 years
  2. খ
    খ) 12, 28, 32 years
  3. গ
    গ) 16, 28, 36 years
  4. ঘ
    ঘ) 14, 28, 36 years
ব্যাখ্যা
Let their present ages be 4x, 7x and 9x years respectively.
Therefore, (4x - 8) + (7x - 8) + (9x - 8) = 56
⇒ 20x = 80
⇒ x = 4
∴ Their present ages are
4x = 16 years,
7x = 28 years and
9x = 36 years respectively.
৩৭২.
The average age of father, mother and daughter is 30 years. The average age of mother and daughter is 25 years. What is the age of father?
  1. ক
    30 years
  2. খ
    40 years
  3. গ
    50 years
  4. ঘ
    35 years
ব্যাখ্যা
Question: The average age of father, mother and daughter is 30 years. The average age of mother and daughter is 25 years. What is the age of father?

Solution:
The average age of father, mother and daughter is 30 years
∴ Total age of father, mother and daughter is (30 × 3) years 
= 90 years 

The average age of mother and daughter is 25 years
∴ Total age of mother and daughter is (25 × 2) years
= 50 years 

∴ The age of father is 90 - 50 years
= 40 years
৩৭৩.
The product of the present ages of Rina and Mina is 1500 years. The ratio of their present ages is 5 : 3. What is the difference of their present ages?
  1. ক
    20 years
  2. খ
    21 years
  3. গ
    22 years
  4. ঘ
    23 years
ব্যাখ্যা
Question: The product of the present ages of Rina and Mina is 1500 years. The ratio of their present ages is 5 : 3. What is the difference of their present ages?

Solution:
Let,
the present age of Rina be 5x and the present age of Mina be 3x

ATQ,
5x × 3x = 1500
⇒ 15x2 = 1500
⇒ x2 = 100
∴ x = 10

∴ the present ages of Rina = (5 × 10) = 50 years
∴ the present ages of Mina = (3 × 10) = 30 years

So, the difference of their present ages = (50 - 30) = 20 years
৩৭৪.
The average age of 8 men is increased by 4 years when one of them whose age is 30 years is replaced by a new man. What is the age of a new man?
  1. ক
    65 years
  2. খ
    57 years
  3. গ
    62 years
  4. ঘ
    76 years
  5. ঙ
    72 years
ব্যাখ্যা
Let, the average age of 8 men be x
Sum of the age of 8 men = 8x
Let, age of new man be y
According to question,
8x + y - 30 = 8 (x + 4)
8x + y - 30 = 8x + 32
y = 8x + 32 + 30 - 8x
y = 62 years

So, Age of the new man is 62 years.
৩৭৫.
Jowel got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Jowel's wife was 10 years younger to him at the time of his marriage. The age of Jowel's wife is-
  1. ক
    32 years
  2. খ
    35 years
  3. গ
    38 years
  4. ঘ
    42 years
  5. ঙ
    None
ব্যাখ্যা
Question: Jowel got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. Jowel's wife was 10 years younger to him at the time of his marriage. The age of Jowel's wife is-

Solution:
Let Jowel's age 8 years ago be x years,
Then, present age = (x + 8) years

ATQ,
x + 8 = 6x/5
⇒ 6x = 5x + 40
⇒ x = 40

Jowel's wife's age 8 years ago = (40 - 10) years
= 30 years

∴ His wife's age now = (30 + 8) years
= 38 years
৩৭৬.
9 years ago a brother was 7 years older than his sister. At present their total age is 53. What is the present age of the sister?
  1. ক
    23 years
  2. খ
    22 years
  3. গ
    24 years
  4. ঘ
    26 years
ব্যাখ্যা
Question: 9 years ago a brother was 7 years older than his sister. At present their total age is 53. What is the present age of the sister?

Solution: 
Let,
sister was x years old 9 years ago.
∴ brother was (x + 7) years old

ATQ,
x + x + 7 + 9 + 9 = 53
or, 2x = 53 - 25
or, x = 14

present age of the sister is = 14 + 9 = 23 years
৩৭৭.
The present ages of three cousins are in the ratio of 5 : 6 : 7. Three years ago, their total age was 45 years. In two years, what will be the age of the youngest cousin?
  1. ক
    15 years
  2. খ
    17 years
  3. গ
    19 years
  4. ঘ
    21 years
ব্যাখ্যা

Question: The present ages of three cousins are in the ratio of 5 : 6 : 7. three years ago, their total age was 45 years. In two years, what will be the age of the youngest cousin?

Solution:
Present age ratio of three cousins is 5 : 6 : 7
Let their ages be 5x, 6x, and 7x, respectively

ATQ,
5x - 3 + 6x - 3 + 7x - 3 = 45
⇒ 18x - 9 = 45
⇒ 18x = 54
⇒ x = 3

∴ The present age of the youngest cousin is = 5x = 3 × 5 = 15 years.
In two years, his age will be = (15 + 2) = 17 years

৩৭৮.
The product of the ages of A and B is 240. If twice the age of B is more than A’s age by 4 years, what was B’s age 2 years ago?
  1. ক
    12 years
  2. খ
    10 years
  3. গ
    8 years
  4. ঘ
    14 years
ব্যাখ্যা
Question: The product of the ages of A and B is 240. If twice the age of B is more than A’s age by 4 years, what was B’s age 2 years ago?

Solution: 
Let A’s present age be x years.
Then, B’s present age = 240/x years

So, according to question
2(240/x ) -  x = 4
⇒ 480 - x2 = 4x
⇒ x2 + 4x - 480 = 0
⇒ (x + 24) (x - 20) = 0
⇒ x = 20

B’s present age = 240/20 = 12 years
Thus, B’s age 2 years ago = 12 - 2 = 10 years
৩৭৯.
Rupa got married 6 years ago. Today her age is 5/4 times her age at the time of marriage. Her son's age is (1/10) times her age. Her son's age is-
  1. ক
    4 years
  2. খ
    1 year
  3. গ
    3 years
  4. ঘ
    7 years
ব্যাখ্যা
Question: Rupa got married 6 years ago. Today her age is 5/4 times her age at the time of marriage. Her son's age is (1/10) times her age. Her son's age is-

Solution:
Let
the age of Rupa before 6 years ago is x.
Then today her age is x + 6 

Now
x + 6 = 5x/4
4x + 24 = 5x
5x - 4x = 24
x = 24 

Now age of  Rupa = 24 + 6 =30 years
Her son's age is = 30/10 ears
= 3 years
৩৮০.
A is two years older than B who is twice as old as C. If the total ages of A, B, and C is 27, how old is C?
  1. ক
    ক) 5 years
  2. খ
    খ) 8 years
  3. গ
    গ) 10 years
  4. ঘ
    ঘ) 15 years
ব্যাখ্যা
Question: A is two years older than B who is twice as old as C. If the total ages of A, B, and C is 27, how old is C?

Solution:
Let, C's age be x years.
Then, B's age = 2x years.
And A's age = (2x + 2) years. 

ATQ,
2x + 2 + 2x + x = 27
⇒ 5x = 25
⇒ x = 5
৩৮১.
Ten years ago, Alif was 1/3rd as old as Joy. If Alif is 18 years old now, how old is Joy now?
  1. ক
    32 years
  2. খ
    38 years
  3. গ
    36 years
  4. ঘ
    34 years
ব্যাখ্যা
Question: Ten years ago, Alif was 1/3rd as old as Joy. If Alif is 18 years old now, how old is Joy now?

Solution:
Let,
Age of Joy now x years

ATQ,
(x - 10)/3 = (18 - 10)
⇒ x - 10 = 24
⇒ x = 34

∴ The age of Joy now 34 years
৩৮২.
The ratio of the present ages of a father and his son is 5 : 1. Five years ago, the ratio was 9 : 1. What will be the father's age five years from now?
  1. ক
    50 years
  2. খ
    60 years
  3. গ
    65 years
  4. ঘ
    55 years
ব্যাখ্যা

Question: The ratio of the present ages of a father and his son is 5 : 1. Five years ago, the ratio was 9 : 1. What will be the father's age five years from now?
 
Solution:
Let the present age of the son = x years
Then present age of the father = 5x years

Five years ago, Father's age = 5x - 5
And son's age = x - 5

According to the question,
(5x - 5) : (x - 5) = 9 : 1
⇒ (5x - 5)/(x - 5) = 9/1
⇒ 5x - 5 = 9(x - 5)
⇒ 5x - 5 = 9x - 45
⇒ 9x - 5x = 45 - 5
⇒ 4x = 40
⇒ x = 40/4 = 10
∴ x = 10

Therefore, present age of son = 10 years
present age of father = 5 × 10 = 50 years

Five years from now father's age = 50 + 5 = 55 years

So the father's age five years from now will be 55 years.

৩৮৩.
The sum of the ages of 5 children born at the intervals of 3 year each is 50 year. What is the age of the youngest child?
  1. ক
    ক) 8 years
  2. খ
    খ) 16 years
  3. গ
    গ) 6 years
  4. ঘ
    ঘ) 4 years
ব্যাখ্যা

Let the age of the youngest child is 'X' year.
Then the child elder than the yongest is 'X + 3' years
Since each have 3years difference upto 5 children
And given that
=> X + X+3 + X+6 + X+9 + X+12 = 50
=> 5X + 30 = 50
=> X = 4 years.

৩৮৪.
The son was born when the father was 25 years old. At what age will the father's age be twice the son's age?
  1. ক
    40 years
  2. খ
    50 years
  3. গ
    60 years
  4. ঘ
    70 years
ব্যাখ্যা
প্রশ্ন: The son was born when the father was 25 years old. At what age will the father's age be twice the son's age?

সমাধান:
পিতার বয়স 2a হলে পুত্রের বয়স হবে a বছর
আবার, পিতা পুত্রের চেয়ে 25 বছরের বড় হলে,
পুত্রের বয়স = 2a - 25 বছর

শর্তমতে,
2a - 25 = a
∴ a = 25

অতএব, পিতার বয়স = 2a বছর
= 2 ×25
= 50 বছর
৩৮৫.
Rahim is 12 years old. He is three times older than Karim. What will be the age of Rahim when he is two times older than Karim?
  1. ক
    ক) 15 years
  2. খ
    খ) 16 years
  3. গ
    গ) 17 years
  4. ঘ
    ঘ) 18 years
ব্যাখ্যা
Question: Rahim is 12 years old. He is three times older than Karim. What will be the age of Rahim when he is two times older than Karim?

Solution: 
Rahim is 12 years old.
He is three times older than Karim. 

karim is = 12 / 3 years
= 4 years

let, Rahim's age will be two times than karim after x years

(12 + x) = 2 (4 + x)
⇒ 12 +x = 8 + 2x
⇒ 2x - x = 12 - 8
∴ x = 4 

Rahim's age will be = 12 + 4 years
= 16 years
৩৮৬.
Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?
  1. ক
    6 years
  2. খ
    4 years
  3. গ
    8 years
  4. ঘ
    12 years
ব্যাখ্যা
Question: Ayesha's father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents?

Solution:
Ayesha's brother is 4 years younger than her.

Ayesha's mother was 36 years old when her brother was born.
So, the age of Ayesha's mother when she was born = 36 - 4 years = 32 years. 
 
And when Ayesha was born her father's age = 38 years

∴ The difference between the ages of her parents = 38 - 32 years
= 6 years
৩৮৭.
A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B?
  1. ক
    ক) 6 years
  2. খ
    খ) 10 years
  3. গ
    গ) 16 years
  4. ঘ
    ঘ) 19 years
ব্যাখ্যা
Let C's age be x years.
Then, B's age = 2x years.
A's age = (2x + 2) years. 
∴ (2x + 2) + 2x + x = 27
⇒ 5x = 25
⇒ x = 5.
Hence,
B's age = 2x = 10 years.
৩৮৮.
If the ratio of present age of Ashik and Vishal is 9 : 4 and their sum of present age is 52 years, find the present age of Vishal.
  1. ক
    16
  2. খ
    17
  3. গ
    18
  4. ঘ
    14
ব্যাখ্যা
Question: If the ratio of present age of Ashik and Vishal is 9 : 4 and their sum of present age is 52 years, find the present age of Vishal.

Solution:
Let, age of Ashik be 9x and age of Vishal be 4x
Then, sum of both ages = 9x + 4x = 13x
⇒ 13x = 52
⇒ x = 4 years

∴ Age of Vishal = 4x = 4 × 4 = 16 years
৩৮৯.
The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the oldest child?
  1. ক
    12 years
  2. খ
    4 years
  3. গ
    16 years
  4. ঘ
    20 years
  5. ঙ
    None of the above
ব্যাখ্যা
Question: The sum of the ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the oldest child?

Solution: 
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
or, 5x = 20
or, x = 4.
∴ Age of the oldest child = x + 12 = 4 + 12 = 16 years.
৩৯০.
The present age of a mother is the thrice that of her daughter. After 13 years, the age of the mother will be twice that of her daughter. The present age of the daughter is-
  1. ক
    ক) 10 years
  2. খ
    খ) 11 years
  3. গ
    গ) 12 years
  4. ঘ
    ঘ) 13 years
ব্যাখ্যা
Question: The present age of a mother is the thrice that of her daughter. After 13 years, the age of the mother will be twice that of her daughter. The present age of the daughter is-

Solution: 
Let
the daughter's present age be x years.
Then, mother  present age = 3x years

According to the question 
3x + 13 = 2 (x + 13)
⇒ 3x + 13 = 2x + 26
⇒ x = 13
Present age of daughter = 13 years
৩৯১.
Mr. A is 5 years senior to Mr. B, Mr. B is 3 years senior to Mr. C, Mr. C is 2 year junior to Mr. D in job experience. If Mr. D has 15 years job experience than how many years of experience possessing Mr. A?
  1. ক
    ক) 18
  2. খ
    খ) 19
  3. গ
    গ) 20
  4. ঘ
    ঘ) 22
  5. ঙ
    ঙ) 21
ব্যাখ্যা
Question: Mr. A is 5 years senior to Mr. B, Mr. B is 3 years senior to Mr. C, Mr. C is 2 year junior to Mr. D in job experience. If Mr. D has 15 years job experience than how many years of experience possessing Mr. A?

Solution:
Job experience of Mr.D = 15 years

Mr. C is 2 year junior to Mr. D in job experience.
∴Job experience of Mr.c = 15 - 2 = 13 years 

Mr. B is 3 years senior to Mr. C in job experience.
∴ Job experience of Mr.b = 13 + 3  = 16 years 

Mr. A is 5 years senior to Mr. B in job experience.
∴ Job experience of Mr.A = 16 + 5 = 21 years
৩৯২.
Ten years ago, Mahin was half the age of Rahul. If the ratio of their present ages is 3 : 4, what is Rahul's present age?
  1. ক
    30 years
  2. খ
    25 years
  3. গ
    15 years
  4. ঘ
    20 years
ব্যাখ্যা
Question: Ten years ago, Mahin was half the age of Rahul. If the ratio of their present ages is 3 : 4, what is Rahul's present age?

Solution: 
let,
the present age of Mahin = 3x years
and the present age of Rahul = 4x years

∴ 10 years ago, Mahin was (3x - 10) years old
∴ 10 years ago, Rahul was (4x - 10) years old 

ATQ, 
2(3x - 10) = 4x - 10
⇒ 6x - 20 = 4x - 10 
⇒ 6x - 4x = 20 - 10 
⇒ 2x = 10 
∴ x = 5 

∴ Present age of Rahul = (4 × 5) = 20 years
৩৯৩.
Tanvir’s present age is two-fifths of the age of his father. After 8 years, Tanvir will be one-half of the age of his father. What is the present age of the father?
  1. ক
    40 years
  2. খ
    41 years
  3. গ
    42 years
  4. ঘ
    43 years
ব্যাখ্যা
Question: Tanvir’s present age is two-fifths of the age of his father. After 8 years, Tanvir will be one-half of the age of his father. What is the present age of the father?

Solution:
Let,
Present age of father = p year
So, Tanvir's present age = p × (2/5) year
  
After 8 years father will be = (p + 8) year
After 8 years Tanvir will be = {(2p/5) + 8} year

According to the conditions,
(1/2)(p + 8) = {(2p/5) + 8}
or, (p + 8)/2 = (2p + 40)/5
or, 5p + 40 = 4p + 80
or, 5p - 4p = 80 - 40
∴ p = 40

So, Present age of father = 40 years.
৩৯৪.
5 years back Himel got married at the age of 30. After 2 years he was blessed with a baby child. What will be the ratio of Himel and his children's age 5 years from now?
  1. ক
    ক) 4 : 1
  2. খ
    খ) 1 : 4
  3. গ
    গ) 5 : 1
  4. ঘ
    ঘ) 5 : 2
ব্যাখ্যা
Question: 5 years back Himel got married at the age of 30. After 2 years he was blessed with a baby child. What will be the ratio of Himel and his children's age 5 years from now?

Solution: 
বর্তমানে হিমেলের বয়স = ৩০ + ৫ = ৩৫ বছর
তার সন্তানের বয়স = ৩ বছর

৫ বছর পর,
হিমেলের বয়স হবে = ৩৫ + ৫ = ৪০ বছর
তার সন্তানের বয়স = ৩ + ৫ = ৮ বছর

অনুপাত = ৪০ : ৮ = ৫ : ১
৩৯৫.
The father explained to his son, “When you were born, I had reached the age you are now.” If the father is 52, what was the son’s age five years ago?
  1. ক
    18 years
  2. খ
    21 years
  3. গ
    23 years
  4. ঘ
    19 years
  5. ঙ
    None
ব্যাখ্যা

Question: The father explained to his son, “When you were born, I had reached the age you are now.” If the father is 52, what was the son’s age five years ago?

Solution:
let, at present son is x years old
so, at time of his birth the father was x years old

∴ at present the age of father is = x + x year
= 2x years

2x = 52
⇒ x = 52/2
= 26 years

∴ the son's age five years back was = 26 - 5
= 21 years

৩৯৬.
Five years ago, Rahul was twice as old as his sister. Now, Rahul is 6 years older than his sister. What is the present age of Rahul?
  1. ক
    22 years
  2. খ
    19 years
  3. গ
    21 years
  4. ঘ
    15 years
  5. ঙ
    17 years
ব্যাখ্যা

Question: Five years ago, Rahul was twice as old as his sister. Now, Rahul is 6 years older than his sister. What is the present age of Rahul?

Solution:
Let,
Present age of Rahul's sister = x years
Present age of Rahul = x + 6 years (since Rahul is 6 years older)

Five years ago,
Rahul’s age = (x + 6) - 5 = x + 1
And sister’s age = x - 5

According to the question,
x + 1 = 2(x - 5)
⇒ x + 1 = 2x - 10
⇒ 2x - x = 10 + 1
∴ x = 11

∴ Rahul's present age = x + 6 = 11 + 6 = 17 years.

৩৯৭.
Five years ago, Rahul was twice as old as his sister. Now, Rahul is 6 years older than his sister. What is the present age of Rahul?
  1. ক
    24 years.
  2. খ
    17 years.
  3. গ
    12 years.
  4. ঘ
    22 years.
  5. ঙ
    None of these
ব্যাখ্যা
Question: Five years ago, Rahul was twice as old as his sister. Now, Rahul is 6 years older than his sister. What is the present age of Rahul?

Solution:
Let,
Present age of Rahul's sister = x years
Present age of Rahul = x + 6 years (since Rahul is 6 years older)

Five years ago,
Rahul’s age = (x + 6) - 5 = x + 1
And sister’s age = x - 5

According to the question,
x + 1 = 2(x - 5)
⇒ x + 1 = 2x - 10
⇒ 2x - x = 10 + 1
∴ x = 11

∴ Rahul's present age = x + 6 = 11 + 6 = 17 years.
৩৯৮.
The average age of 80 boys in a class is 15. The average age of a group of 20 boys in the class is 16 and the average age of another 25 boys in the class is 14. What is the average age of the remaining boys in the class?
  1. ক
    ক) 15.14 yrs.
  2. খ
    খ) 16.25 yrs.
  3. গ
    গ) 17.15 yrs.
  4. ঘ
    ঘ) 18.10 yrs.
ব্যাখ্যা
Total ages of 80 boys = 15 × 80 = 1200 yrs.
Total age of20 boys = 16 × 20 = 320 yrs
Total age of 25 boys = 14  × 25 = 350 yrs.

Average age of remaining boys = {1200 - (320 + 350)}/ {80 - (25 + 20)}
                                                   = 530/35
                                                    = 15.14 yrs.
৩৯৯.
A is two years older than B, who is twice as old as C. If the total of the ages of A, B, and C is 32, how old is A?
  1. ক
    10 years
  2. খ
    12 years
  3. গ
    14 years
  4. ঘ
    16 years
ব্যাখ্যা
Question: A is two years older than B, who is twice as old as C. If the total of the ages of A, B, and C is 32, how old is A?

Solution:
Let,
C's age be = a years
Then, B's age = 2a years
A's age = (2a + 2) years

∴ (2a + 2) + 2a + a = 32
⇒ 5a = 30
⇒ a = 6
Hence, A's age = (2 × 6) + 2 = 14 years.
৪০০.
The combined average age of a husband, wife, and child was 27 years three years back, and the average age of the wife and child was 20 years five years ago. Find their(wife and child) current total age.
  1. ক
    30 years
  2. খ
    35 years
  3. গ
    40 years
  4. ঘ
    50 years
ব্যাখ্যা
Question: The combined average age of a husband, wife, and child was 27 years three years back, and the average age of the wife and child was 20 years five years ago. Find their(wife and child) current total age.

Solution:
Sum of the present ages of husband, wife and child =(27 × 3 + 3 × 3) years
= (81 + 9) years
= 90 years

Sum of the present ages of wife and child =(20 × 2 + 5 × 2) years
= (40 + 10) years
= 50 years