Problems on Ages

PrepBank · পাতা ৫ / ৭ · ৪০১–৫০০ / ৬০৭

৪০১.

10 years ago, P was half of Q in age. If the ratio of their present age is 3 : 4. What will be the average present age of them?

ক
ক) 35 years
খ
খ) 30 years
গ
গ) 17.5 years
ঘ
ঘ) 22.5 years

ব্যাখ্যা

Let, the age of P be x years 10 years ago and so the age of Q is 2x years.
present age of P and Q are x + 10 and 2x + 10
(x + 10)/(2x + 10) = 3/4
⇒ 6x + 30 = 4x + 40
⇒ 2x = 10
⇒ x = 5
the average present age of them
= (x + 10 + 2x + 10)/2
= (5 + 10 + 2 × 5 + 10)/2
= 17.5 years

৪০২.

The present age of a mother is 3 years more than three times the age of her daughter. Three years hence, the mother’s age will be 10 years more than twice the age of the daughter. Find the present age of the mother.

ক
23 years
খ
27 years
গ
30 years
ঘ
33 years

ব্যাখ্যা

Question: The present age of a mother is 3 years more than three times the age of her daughter. Three years hence, the mother’s age will be 10 years more than twice the age of the daughter. Find the present age of the mother.

Solution:
Let the daughter’s present age be ‘n’ years.
∴ Mother’s present age = (3n + 3) years

So, according to the question
(3n + 3 + 3) = 2 (n + 3) + 10
⇒ 3n + 6 = 2n + 16
⇒ n = 10

Hence, mother’s present age = (3n + 3) = ((3 × 10) + 3) years = 33 years

৪০৩.

Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?

ক
1.5 times
খ
3 times
গ
2 times
ঘ
2.5 times

ব্যাখ্যা

Question: Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit's age. After further 8 years, how many times would he be of Ronit's age?

Solution:
Let,
Ronit's present age be x years.
Then, father's present age =(x + 3x) years
= 4x years.

ATQ,
(4x + 8) = {5(x + 8)}/2
⇒ 8x + 16 = 5x + 40
⇒ 3x = 24
∴ x = 8

Now, (4x + 16)/(x + 16) = 48/24 = 2
∴ Father would be 2 times of Ronit's age.

৪০৪.

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, then how old is B?

ক
ক) 12 years
খ
খ) 14 years
গ
গ) 10 years
ঘ
ঘ) 8 years

ব্যাখ্যা

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

Now
(2x + 2) + 2x + x = 27
5x = 25
x = 5

Hence, B's age = 2x = 10 years

৪০৫.

The average age of 8 children of a family is 12 yr. If the age of 7 children is 12, 8, 14, 11, 9, 13 and 15 yr, then the age of 8th child will be-

ক
12 yr
খ
14 yr
গ
13 yr
ঘ
15 yr
ঙ
None of above

ব্যাখ্যা

Total age of 8 children = 8 x 12 = 96 yr
Total age of 7 children = 12 + 8 + 14 + 11 + 9 + 13 + 15 = 82
The age of 8th child = 96 - 82 = 14 yr

৪০৬.

20 years ago, my age was 1/3 of what it is now. What is my present age?

ক
ক) 66 years
খ
খ) 36 years
গ
গ) 33 years
ঘ
ঘ) 35 years
ঙ
ঙ) 30 years

ব্যাখ্যা

Let the present age be x years.
20 years ago my age was x - 20.

According to given data,
x - 20 = x/3
=> 2x = 60
=> x = 30

৪০৭.

The ratio of a man's age and his son's age is 7 : 3 and the product of their ages is 756. The ratio of their age after 6 years will be -

ক
ক) 2 : 1
খ
খ) 3 : 1
গ
গ) 5 : 3
ঘ
ঘ) 4 : 3

ব্যাখ্যা

Question: The ratio of a man's age and his son's age is 7 : 3 and the product of their ages is 756. The ratio of their age after 6 years will be -

Solution:
Let, man's age be = 7x years
Then, son's age = 3x years

ATQ,
7x × 3x = 756
⇒ 21x² = 756
⇒ x² = 36
⇒x = 6

The ratio of their ages after 6 years = (7 × 6 + 6) : (3 × 6 + 6)
= 48 : 24
= 2 : 1

৪০৮.

The difference between the present ages of Abir and Deepak is 14 years. Eight years ago, the ratio of their ages was 5 : 7 respectively. What is Deepak's present age?

ক
ক) 55 years
খ
খ) 56 years
গ
গ) 57 years
ঘ
ঘ) 58 years

ব্যাখ্যা

Let the age of Abir eight years ago be 5x
Let the age of Deepak eight years ago be 7x
Present age of Abir would be 5x + 8
Present age of Deepak would be 7x + 8

According to question,
7x + 8 - (5x + 8) = 14
7x + 8 - 5x - 8 = 14
2x = 14
x = 7

Deepak's present age = 7 × 7 + 8 = 57 years

৪০৯.

The ages of A and B are in the ratio 6:5 and the sum of their ages is 44 years. What will be the ratio of their ages after 8 years?

ক
ক) 7:6
খ
খ) 8:7
গ
গ) 9:8
ঘ
ঘ) 3:4

ব্যাখ্যা

A's age = 44 × (6/11) years = 24 years and
B's age = (44 - 24) years = 20 years.
Ratio of their ages after 8 years = (24 + 8)/(20 + 8)
= 32/28
= 8/7
= 8:7

৪১০.

The sum of the present age of mother and her son is 60 years. Six years ago, the age of the mother was five times the age of her son. What will be the age of her son after 6 years?

ক
23 years
খ
22 years
গ
21 years
ঘ
20 years

ব্যাখ্যা

Question: The sum of the present age of mother and her son is 60 years. Six years ago, the age of the mother was five times the age of her son. What will be the age of her son after 6 years?

Solution:
Let the present age of the son =x
Then, the present age of the mother =(60-x)
As per question:
Six years ago mother's age was 5 times the age of her son:
So, (60-x) -6=5(x-6)
54 - x = 5x -30
84=6x
x=84/6
x=14 Years

Age of son after 6 years
=x+6
=14+6
=20 Years

৪১১.

The present ages of Samba and Bambi are in the ratio of 6:4. Five years ago their ages were in the ratio of 5:3. How old is samba?

ক
ক) 30
খ
খ) 36
গ
গ) 42
ঘ
ঘ) 48
ঙ
ঙ) 46

ব্যাখ্যা

Bambi’s present age = 6x,
Samba’s present age = 4x
Therefore,
(6x - 5)/(4x - 5) = 5/3
Or, 20x - 25 = 18x - 15
So, x = 5
And samba’s age = 6 × 5 = 30

৪১২.

If Ehsan was 22 years old x years ago and Shaon will be 24 years old in y years, what was the average of their ages 4 years ago?

ক
(x - y + 42)/2
খ
(x - y + 38)/2
গ
(x - y )/2
ঘ
(x + y )/2

ব্যাখ্যা

Question: If Ehsan was 22 years old x years ago and Shaon will be 24 years old in y years, what was the average of their ages 4 years ago?

Solution:
Ehsan was 22 years old x years ago
present age = x + 22 years
4 years ago, his age was = x + 22 - 4 = x + 18 years

Shaon will be 24 years old in y years
4 years ago, his age was = 24 - y - 4
= 20 - y years

average 4 years ago = (x + 18 + 20 - y)/2
= (x - y + 38)/2

৪১৩.

The sum of the ages of a mother and daughter is 56 years. Four years ago, the mother was five times as old as her daughter. Find the present age of the daughter is?

ক
12 years
খ
18 years
গ
8 years
ঘ
15 years

ব্যাখ্যা

Question: The sum of the ages of a mother and daughter is 56 years. Four years ago, the mother was five times as old as her daughter. Find the present age of the daughter is?

Solution:
Let daughter's present age = x years
Then mother's present age = (56 - x) years

Four years ago:
Daughter's age = x - 4
Mother's age = (56 - x) - 4 = 52 - x

ATQ,
⇒ 52 - x = 5(x - 4)
⇒ 52 - x = 5x - 20
⇒ 52 + 20 = 5x + x
⇒ 72 = 6x
∴ x = 12

So the daughter's present age is 12 years.

৪১৪.

Four years ago, the average age of A and B was 16 years. At present the average age of A, B and C is 23 years. What would be the age of C after 4 years.

ক
ক) 29 years
খ
খ) 31 years
গ
গ) 32 years
ঘ
ঘ) 33 years

ব্যাখ্যা

Sum of the ages of A and B, 4 years ago = 16 × 2 = 32 years
Sum of the present age of A and B = 4 + 4 + 32 = 40 years
Sum of the present ages of A, B and C = 23 × 3 = 69 years

⇒ Present age of C = 69 - 40 = 29 years

∴ C's age after 4 years = 29 + 4 = 33 years.

৪১৫.

The sum of the present ages of a son and his father is 70 years. After 5 years, the age of the father will be three times that of the son. At present, their ages are?

ক
10 years, 60 years
খ
12 years, 56 years
গ
12 years, 58 years
ঘ
15 years, 55 years

ব্যাখ্যা

Question: The sum of the present ages of a son and his father is 70 years. After 5 years, the age of the father will be three times that of the son. At present, their ages are?

Solution:
Let,
The son's age is x years.
Then, father's age = (70 - x) years.

ATQ,
(70 - x) + 5 = 3(x + 5)
⇒ 75 - x = 3x + 15
⇒ 4x = 60
∴ x = 15

∴ Son's age = 15 years
And the father's age = (70 - 15) = 55 years.

৪১৬.

P is five years younger than Q, who is twice as old as R. If the sum of their ages is 55, how old is Q?

ক
12 years
খ
24 years
গ
36 years
ঘ
40 years

ব্যাখ্যা

Question: P is five years younger than Q, who is twice as old as R. If the sum of their ages is 55, how old is Q?

Solution:
Let,
the age of R be = x years
Then,
the age of Q = 2x years
and age of P = (2x – 5) years

According to the question,
(2x – 5) + 2x + x = 55
⇒ 5x – 5 = 55
⇒ 5x = 60
⇒ x = 12

Hence, age of Q = 2x = (2 × 12) years = 24 years

৪১৭.

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.

ক
11 : 7
খ
9 : 5
গ
7 : 4
ঘ
7 : 3
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]
⇒ 3x + 20 = 2x + 40

∴ x = 20

∴ (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.

৪১৮.

5 year ago Sushma was 5 times as old as her Son. 5 year hence her age will be 8 less than three times the corresponding age of her Son. Find their ages?

ক
ক) 24 and 13 year
খ
খ) 48 and 24 year
গ
গ) 35 and 11 year
ঘ
ঘ) 33 and 15 year

ব্যাখ্যা

Let the age of sushma be x and
the age of her son is y
Then five year before x-5=5(y-5) ...(1)
Five year hence x+5 = 3(y+5)-8 .....(2)
By soving (1) & (2), we get
5y - 15 = 3y + 7
y = 11
=> x = 35
Therefore, the age of Sushma = 35 and her son = 11.

৪১৯.

At present, the ratio between the ages of Nehal and Rahat is 5 : 4. After 6 years, Nehal's age will be 26 years. What is the age of Rahat at present?

ক
21 years
খ
19 years
গ
18 years
ঘ
16 years

ব্যাখ্যা

Question: At present, the ratio between the ages of Nehal and Rahat is 5 : 4. After 6 years, Nehal's age will be 26 years. What is the age of Rahat at present?

Solution:
Let,
the present ages of Nehal and Rahat be 5x years and 4x years respectively.

ATQ,
5x + 6 = 26
⇒ 5x = 20
∴ x = 4

∴ Rahat's age = 4x = (4 × 4) = 16 years

৪২০.

A son's present age is three-sevenths of his father’s age. After 7 years, he will be half of his father’s age. Find the present age of the father.

ক
39 years
খ
49 years
গ
47 years
ঘ
59 years
ঙ
56 years

ব্যাখ্যা

Question: A son's present age is three-sevenths of his father’s age. After 7 years, he will be half of his father’s age. Find the present age of the father.

Solution:
Let, the father's present age be x years

Then, the son's present age (3x/7) years

∴ (3x/7) + 7 = (1/2) × (x + 7)
⇒ (3x + 49)/7 = (1/2) × (x + 7)
⇒ 7x + 49 = 6x + 98
⇒ x = 49

∴ the present age of the father is 49 years.

৪২১.

Mitu is 60 years old and Ritu is 80 years old. How many years ago their age ratio was 4 : 6?

ক
20 years
খ
22 years
গ
25 years
ঘ
18 years

ব্যাখ্যা

Question: Mitu is 60 years old and Ritu is 80 years old. How many years ago their age ratio was 4 : 6?

Solution:
Let us assume x years ago.
At present, Mitu is 60 years old
and Ritu is 80 years old.
X years ago, Mitu’s age = (60 - x) and Ritu’s age (80 - x)

ATQ,
(60 - x)/(80-x) = 4/6
⇒ 6(60 - x) = 4(80 - x)
⇒ 360 - 6x = 320 - 4x
⇒ 6x - 4x = 360 - 320
⇒ 2x = 40
∴ x = 20

Therefore, 20 years ago their age ratio was 4 : 6.

৪২২.

Rafi is as much younger than Sagar as he is older than Piyal. If the sum of the ages of Piyal and Sagar is 66 years, and Sagar's age is 48 years, then what is the difference between Rafi and Piyal's age?

ক
10 years
খ
12 years
গ
15 years
ঘ
18 years

ব্যাখ্যা

Question: Rafi is as much younger than Sagar as he is older than Piyal. If the sum of the ages of Piyal and Sagar is 66 years, and Sagar's age is 48 years, then what is the difference between Rafi and Piyal's age?

Solution:
Sagar's age is 48 years
the sum of the ages of Piyal and Sagar is 66 years
∴ The age of Piyal is = 66 - 48 year
= 18 year

let, age of rafi is x

48 - x = x - 18
⇒ 2x = 66
∴ x = 33
the difference between Rafi and Piyal's age is = 33 - 18
= 15 years

৪২৩.

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 -

ক
40 years
খ
35 years
গ
50 years
ঘ
55 years

ব্যাখ্যা

Sum of the present ages of husband, wife and child = {(27 × 3) + (3 × 3)} years = 90 years.

Sum of the present ages of wife and child = {(20 × 2) + (5 × 2)} years = 50 years.

Husband's present age = (90 - 50) years = 40 years

৪২৪.

Shuvo is 60 years old and Rubel is 80 years old. How many years ago their age ratio was 4 : 6?

ক
10 years
খ
20 years
গ
15 years
ঘ
25 years

ব্যাখ্যা

প্রশ্ন: Shuvo is 60 years old and Rubel is 80 years old. How many years ago their age ratio was 4 : 6?

সমাধান:

Let x years ago their age ratio was 4 : 6

ATQ,

(60 - x)/(80 - x) = 4/6

⇒ 6 × (60 - x) = 4 × (80 - x)

⇒ 360 - 6x = 320 - 4x

⇒ 6x – 4x = 360 – 320

⇒ 2x = 40

∴ x = 20

Therefore, 20 years ago their age ratio was 4 : 6

৪২৫.

Robi is 10 years older than Kazi. However, 5 years ago Robi was twice as old as Kazi. How old is Kazi now?

ক
5 years
খ
10 years
গ
12 years
ঘ
15 years

ব্যাখ্যা

Question: Robi is 10 years older than Kazi. However, 5 years ago Robi was twice as old as Kazi. How old is Kazi now?

Solution:
Let,
The age of Kazi is x years
∴ The age of Robi is x + 10 years
5 years ago the age of Kazi was x - 5 years
5 years ago the age of Robi was x +10 - 5 years = x + 5 years

ATQ,
2(x - 5) = x + 5
⇒ 2x - 10 = x + 5
⇒ x = 15

∴ The age of Kazi is 15 years

৪২৬.

In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, then the present age of A is-

ক
ক) 39 years
খ
খ) 41 years
গ
গ) 48 years
ঘ
ঘ) 52 years

ব্যাখ্যা

Question: In 10 years, A will be twice as old as B was 10 years ago. If A is now 9 years older than B, then the present age of A is-

Solution:
Let the present age of B be x years.
Then, the present age of A would be (x + 9) years.
After 10 years, the age of A would be (x + 9 + 10) = (x + 19) years and before then years, the age of B was (x - 10) years.

Now,
(x + 19) = 2(x - 10)
x + 19 = 2x - 20
x = 19 + 20 = 39 years

The present age of B is 39 years

The present age of A is 39 + 9 = 48 years

৪২৭.

Shorna'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?

ক
4 years
খ
5 years
গ
6 years
ঘ
8 years

ব্যাখ্যা

প্রশ্ন: Shorna'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?

সমাধান:
স্বর্ণার ভাই তার থেকে ৪ বছরের ছোট।

স্বর্ণার ভাইয়ের জন্মের সময় তার মায়ের বয়স ছিল ৩৬ বছর
তাহলে স্বর্ণার জন্মের সময় তার মায়ের বয়স ছিল ৩৬ - ৪ বছর = ৩২ বছর

এবং স্বর্ণার জন্মের সময় তার বাবার বয়স ছিল ৩৮ বছর

তার বাবা মায়ের বয়সের পার্থক্য = ৩৮ - ৩২ বছর
= ৬ বছর

৪২৮.

A man's age is now 3 times his son's age. Eight years back, the man's age was 5 times his son's age. What is the present age of the son?

ক
ক) 15
খ
খ) 20
গ
গ) 18
ঘ
ঘ) 16

ব্যাখ্যা

Question: A man's age is now 3 times his son's age. Eight years back, the man's age was 5 times his son's age. What is the present age of the son?

Solution:
Let Man's son's present age = x
Man's present age = 3x

According to the question
5(x - 8) = 3x - 8
⇒ 5x - 40 = 3x - 8
⇒ 5x - 3x = 40 - 8
⇒ 2x = 32
x = 16

৪২৯.

The average age of A, B and C is 30 years. If the difference between B’s age and A’s age is the same as the difference between C’s age and B’s age. If D is 40 years older than B then what is the sum of the age of B and D?

ক
ক) 130 years
খ
খ) 60 years
গ
গ) 75 years
ঘ
ঘ) 100 years

ব্যাখ্যা

A + B + C = 30×3 = 90 yrs ...... (1)
ATQ,
B - A = C - B
Or, A+C = 2B
From (1),
B + 2B = 90
Or, B = 30
∴ D = B + 40 = 30 + 40 = 70
So, B + D = 30+70 = 100 yrs

৪৩০.

The sum of the ages of a father and son is 68 years. Four years ago, the father was five times as old as his son. What is the present age of the son?

ক
12 years
খ
14 years
গ
16 years
ঘ
20 years

ব্যাখ্যা

Question: The sum of the ages of a father and son is 68 years. Four years ago, the father was five times as old as his son. What is the present age of the son?

Solution:
ধরি, পুত্রের বর্তমান বয়স = x বছর
তাহলে, পিতার বর্তমান বয়স = (68 - x) বছর

চার বছর আগে,
পুত্রের বয়স ছিল = (x - 4) বছর
পিতার বয়স ছিল = (68 - x) - 4 = (64 - x) বছর

প্রশ্নমতে,
64 - x = 5(x - 4)
⇒ 64 - x = 5x - 20
⇒ 64 + 20 = 5x + x
⇒ 84 = 6x
⇒ x = 84/6
⇒ x = 14

সুতরাং, পুত্রের বর্তমান বয়স হলো 14 বছর।

৪৩১.

The average age of P, Q, R, S and T is 32 years. The average age of P and Q is 28 years, and the average age of R and S is 35 years. What is the age of T?

ক
34 years
খ
30 years
গ
36 years
ঘ
40 years

ব্যাখ্যা

Question: The average age of P, Q, R, S and T is 32 years. The average age of P and Q is 28 years, and the average age of R and S is 35 years. What is the age of T?

Solution:
Given that,
There are 5 people P, Q, R, S, T
Average age of all five = 32 years
Total age of all five = 5 × 32 = 160 years

And,
Average age of P and Q = 28 years
So, age of (P + Q) = 2 × 28 = 56 years

Average age of R and S = 35 years
So, age of (R + S) = 2 × 35 = 70 years

∴ Now, total age of (P + Q + R + S) = 56 + 70 = 126 years

Age of T = Total age of all five - Age of (P + Q + R + S)
= 160 - 126
= 34 years

So the age of T is 34 years.

৪৩২.

A brother was 7 years senior to his sister 9 years ago. Their ages together add up to 53 at present. Find the sister’s and brother's current age.

ক
26 years, 38 years
খ
24 years, 36 years
গ
23 years, 30 years
ঘ
22 years, 42 years

ব্যাখ্যা

Question: A brother was 7 years senior to his sister 9 years ago. Their ages together add up to 53 at present. Find the sister’s and brother's current age.

Solution:
Let the brother's present age be b and the sister's present age be s.

9 years ago:
Brother's age: b - 9
Sister's age: s - 9

Given,
b - 9 = (s - 9) + 7
⇒ b - 9 = s - 2
⇒ b = s + 7

b + s = 53
⇒ b = s + 7
⇒ (s + 7) + s = 53
⇒ 2s + 7 = 53
⇒ 2s = 46
⇒ s = 23

The sister's present age is 23 years.

Brother's present age is 30 years.

৪৩৩.

The sum of the ages of David and Farid is y years. If David is 12 years older than Farid , how many years old will Farid be y years from now, in terms of y?

ক
y - 6
খ
2y - 6
গ
(y/2) - 6
ঘ
(3y/2) - 6
ঙ
(5y/2) - 6

ব্যাখ্যা

Question: The sum of the ages of David and Farid is y years. If David is 12 years older than Farid , how many years old will Farid be y years from now, in terms of y?

Solution:
The sum of the ages of David and Farid is y years: d + f = y;
David is 12 years older than Farid: d = f + 12.

Subtract one from another: f = y - f - 12
⇒ f = (y/2) - 6.

y years from now, Farid will be f + y = (y/2) - 6 + y
= (3y/2) - 6 years old.

৪৩৪.

The sum of the present ages of two persons A and B is 60. If the age of A is twice that of B, find the sum of their ages 5 years hence?

ক
ক) 50
খ
খ) 60
গ
গ) 70
ঘ
ঘ) 80

ব্যাখ্যা

According to the question,
A + B = 60,
A = 2B
2B + B = 60
⇒ B = 20 then A = 40.

5 years,
their ages will be 45 and 25.
Sum of their ages = 45 + 25
= 70.

৪৩৫.

The average age of a man and his son is 34 years. If the respective ratio of their ages after four years 14 : 5. What is the present age of the man?

ক
ক) 48 years
খ
খ) 40 years
গ
গ) 52 years
ঘ
ঘ) 60 years

ব্যাখ্যা

Question: The average age of a man and his son is 34 years. If the respective ratio of their ages after four years 14 : 5. What is the present age of the son?

Solution:
Total age of the man and his son = 34 × 2 = 68 years

Let the man's age be x years
So, the son's age is = 68 - x years

Now,
(x + 4) / (68 - x + 4) = 14/5
⇒ 5x + 20 = 1008 - 14x
⇒ 19x = 988
⇒ x = 52

৪৩৬.

Present ages of A,B and C are in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. What are their present ages (in years)?

ক
ক) 16, 30, 40
খ
খ) 16, 28, 40
গ
গ) 16, 26, 38
ঘ
ঘ) 16, 28, 36

ব্যাখ্যা

Let present ages of A, B, and C be 4x, 7x, and 9x respectively.
(4x − 8) + (7x − 8) + (9x 8) = 56
20x = 80
x = 4

Hence present ages of A, B, and C are (4 × 4), (7 × 4), and (9 × 4)
That is 16, 28, and 36.

৪৩৭.

Maruf, Salman, and Mir-Jafor have taught history for a combined total of 96 years. If Maruf has taught for 9 more years than Salman and for 9 fewer years than Mir-Jafor, for how many years has Mir-Jafor taught?

ক
23
খ
32
গ
35
ঘ
41
ঙ
44

ব্যাখ্যা

Question: Maruf, Salman, and Mir-Jafor have taught history for a combined total of 96 years. If Maruf has taught for 9 more years than Salman and for 9 fewer years than Mir-Jafor, for how many years has Mir-Jafor taught?

Solution:
Let number of years taught by Maruf = M
number of years taught by Salman = S
number of years taught by Mir-Jafor = J

M + S + J = 96 .......(1)

M = S + 9
⇒ S = M - 9 .......(2)

M = J - 9

from (2) ⇒
S = (J - 9) - 9 = J - 18

From(1) ⇒
J - 9 + J - 18 + J = 96
⇒ 3J = 96 + 27 = 123
∴ J = 41

৪৩৮.

Maruf was asked to state his age in years. His reply was, "Take my age 3 years hence, multiply it by 3 and then subtract 3 times my age 3 years ago, and you will know one third of my age". What is the age of maruf?

ক
48 years
খ
54 years
গ
56 years
ঘ
None of the above

ব্যাখ্যা

প্রশ্ন: Maruf was asked to state his age in years. His reply was, "Take my age 3 years hence, multiply it by 3 and then subtract 3 times my age 3 years ago, and you will know one third of my age". What is the age of maruf?

সমাধান:

Let the age of maruf = x years

Then,

⇒ 3(x + 3) - 3(x - 3) = x

⇒ 3x + 9 - 3x + 9 = x

⇒ x = 18

ATQ,
x/3 = 18
∴ x = 18 × 3 = 54 years

∴ The age of maruf is 54 years.

৪৩৯.

The age of the father ten years ago was thrice the age of his son. Ten years hence, the father's age will be twice the age of his son. What is the ratio of their present ages?

ক
7 : 3
খ
1 : 5
গ
7 : 9
ঘ
9 : 2
ঙ
3 : 2

ব্যাখ্যা

Question: The age of the father ten years ago was thrice the age of his son. Ten years hence, the father's age will be twice the age of his son. What is the ratio of their present ages?

Solution:
Let,
son's age 10 years ago be x years.
Then, father’s age 10 years ago = 3x years.

Son's present age = (x + 10) years
Father's present age = (3x + 10) years.

according to the question,
(3x + 10) + 10 = 2 (x + 10 + 10)
⇒ 3x + 20 = 2 (x + 20)
⇒ 3x + 20 = 2x + 40
∴ x = 20

Ratio of present ages of father and the son
= (3x + 10)/(x + 10)
= {(3 × 20) + 10}/(20 + 10)
= 70/30
= 7 : 3

৪৪০.

Rajan got married 10 years ago. His present age is (6/5) times of his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marrige. The present age of Rajan's sister is = ?

ক
ক) 40 year
খ
খ) 50 year
গ
গ) 60 year
ঘ
ঘ) 70 year

ব্যাখ্যা

Question: Rajan got married 10 years ago. His present age is (6/5) times of his age at the time of his marriage. Rajan's sister was 10 years younger to him at the time of his marrige. The present age of Rajan's sister is = ?

Solution:
Present age of Rajan is = x year

x = (6/5) (x - 10)
⇒ 5x = 6x - 60
⇒ 6x - 5x = 60
⇒ x = 60 years

at time of marriage, rajan's age is 60 - 10 = 50 years
at time of marriage, rajan's sister age is = 50 - 10 years = 40 years

∴ The present age of rajan's sister age is = 40 + 10 = 50 year

৪৪১.

The age of a man is 4 times of his son. Five years ago, the man was nine times old as his son was at that time. The present age of man is?

ক
30
খ
32
গ
34
ঘ
36

ব্যাখ্যা

Question: The age of a man is 4 times of his son. Five years ago, the man was nine times old as his son was at that time. The present age of man is?

Solution:
Let the son's age be x years and the father's age be 4x years

ATQ,
4x - 5 = 9(x - 5)
⇒ 4x - 5 = 9x - 45
⇒ 5x = 40
∴ x = 8

∴ Present age of the father = 4 × 8 = 32 years

৪৪২.

Ten years ago, a man was six times as old as his son. Two years hence, twice his age will be equal to four times the age of his son. What is the presesnt age of the son?

ক
11 years
খ
12 years
গ
13 years
ঘ
14 years

ব্যাখ্যা

Question: Ten years ago, a man was six times as old as his son. Two years hence, twice his age will be equal to four times the age of his son. What is the presesnt age of the son?

Solution:
Let,
Son's age 10 years ago be a years.
then, man's age 10 years ago = 6a years

∴ Son's present age = (a + 10) years
And man's present age = (6a + 10) years

ATQ, 2{(6a + 10) + 2} = 4{(a + 10) + 2}
⇒ 2(6a + 12) = 4(a + 12)
⇒ 12a + 24 = 4a + 48
⇒ 12a - 4a = 48 - 24
⇒ 8a = 24
⇒ a = 3

So, son's present age = (a + 10) = 3 + 10 = 13 years.

৪৪৩.

P is now 8 years older than Q. 17 years ago P was twice as old as Q. How old will Q be in 10 years?

ক
ক) 43
খ
খ) 35
গ
গ) 15
ঘ
ঘ) 27

ব্যাখ্যা

Question: P is now 8 years older than Q. 17 years ago, P was twice as old as Q. How old will Q be in 10 years?

Solution:
ধরি,
১৭ বছর পূর্বে Q এর বয়স ছিল = ক বছর
১৭ বছর পূর্বে P এর বয়স ছিল = ২ক বছর

প্রশ্নমতে,
২ক + ১৭ = ক + ১৭ + ৮
২ক - ক = ৮
ক = ৮ বছর

১০ বছর পর Q এর বয়স হবে = ক + ১৭ + ১০
= ৮ + ২৭
= ৩৫ বছর

৪৪৪.

The ratio of Rohan’s age 4 years ago and Rahul’s age after 4 years is 1 : 1. If at present, the ratio of their ages is 5 : 3, then find the ratio between Rohan’s age 4 years hence and Rahul’s age 4 years ago.

ক
ক) 1 : 3
খ
খ) 3 : 1
গ
গ) 4 : 3
ঘ
ঘ) 3 : 4

ব্যাখ্যা

If ages in the numerical are mentioned in the ratio A : B, then A: B will be Ax and Bx
1) At present : Ratio of their ages = 5 : 3. Therefore, 5 : 3 will be 5x and 3x.
Rohan's age 4 years ago = 5x – 4
Rahul's age after 4 years = 3x + 4

2)Ratio of Rohan’s age 4 years ago and Rahul's age after 4 years is 1: 1
Therefore,
(5x - 4)/(3x + 4) = 1/1
⇒ 5x - 4 = 3x + 4
⇒ 5x - 3x = 4 + 4
⇒ 2x = 8
⇒ x = 4
Solving, we get x = 4

3)We are asked to find the ratio between Rohan's age 4 years hence and Rahul's age 4 years ago.
Rohan's age : (5x + 4)
Rahul's age: (3x – 4)
Ratio of Rohan's age and Rahul’s age
(5x + 4)/(3x - 4) = 24/8
(5x + 4)/(3x - 4) = 3/1
(5x + 4) : (3x - 4) = 3 : 1.

৪৪৫.

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?

ক
ক) 30 years
খ
খ) 35 years
গ
গ) 40 years
ঘ
ঘ) 45 years

ব্যাখ্যা

Let A’s age 10 years ago be = x years
Then, B’s age 10 years ago = 2x years
ATQ, (x + 10) / (2x + 10) = 3/4
Or, 6x + 30 = 4x + 40
Or, x = 5
So, the total of their present ages = (x + 10 + 2x + 10) = (5 + 10 + 2.5 + 10) = 35 years.

৪৪৬.

The ratio of Present age of Madhu and Divya is 6:7. Madhu is 7 years younger than Laxmi. Laxmi’s age after 8 years will be 51 years. Then what is the difference between the present ages of Madhu and Divya?

ক
2
খ
3
গ
4
ঘ
5
ঙ
6

ব্যাখ্যা

Laxmi present age = 51 - 8 = 43
So Madhu Age = (43 - 7) = 36
So, Diviya Present Age = 36 × 7/6 = 42
So Difference = (42 - 36) = 6 years

৪৪৭.

The average age of A, B, C, D & E is 40 years. The average age of A and B is 35 years and the average of C and D is 42 years. Age of E is

ক
ক) 48
খ
খ) 46
গ
গ) 42
ঘ
ঘ) 45
ঙ
ঙ) 47

ব্যাখ্যা

Sum of their ages = 40 × 5 = 200 years
Sum of A & B’s ages = 35 × 2 = 70 years
Sum of C & D’s ages = 42 × 2 = 84
So, Age of E = 200 - (70 + 84) = 46

৪৪৮.

The ratio of the current ages of Momen and his brother is 15:14. The ratio of the ages of Momen and his sister in 6 years will be 18:19. The gap between Momens age and his sister is the same as the gap between Momens age and his brother. What is Momens current age?

ক
29 years
খ
32 years
গ
30 years
ঘ
31 years

ব্যাখ্যা

Question: The ratio of the current ages of Momen and his brother is 15:14. The ratio of the ages of Momen and his sister in 6 years will be 18:19. The gap between Momens age and his sister is the same as the gap between Momens age and his brother. What is Momens current age?

Solution:
Let's say Momen's current age is x
From the first ratio (Momen : Brother = 15 : 14) If Momen's age is x, then his brother's age is (14x/15)
Let's say Momen's sister's age is y

Given that the gap between Momen and sister is same as gap between Momen and brother
|x - y| = |x - (14x/15)|
|x - y| = |x - 14x/15|
|x - y| = |15x/15 - 14x/15|
|x - y| = x/15 ...... (1)

After 6 years, the ratio of Momen:Sister will be 18:19
(x + 6)/(y + 6) = 18/19
19(x + 6) = 18(y + 6)
19x + 114 = 18y + 108
19x = 18y - 6
y = (19x + 6)/18 .......... (2)

From equations 1 and 2 ⇒
x - y = x/15 (since y is less than x)
x - (19x + 6)/18 = x/15
18x - 19x - 6 = 18x/15
-x - 6 = 18x/15
-15x - 90 = 18x
-33x = 90
x = 30

Therefore, Momen's current age is 30 years.

৪৪৯.

Twelve years ago, Babu was twice as old as Rakib. If the ratio of their present ages is 4 : 3 respectively, find the difference between their present ages.

ক
5 years
খ
6 years
গ
7 years
ঘ
8 years

ব্যাখ্যা

Question: Twelve years ago, Babu was twice as old as Rakib. If the ratio of their present ages is 4 : 3 respectively, find the difference between their present ages.

Solution:
Let 12 years ago age of Rakib was X years and age of Babu was 2X.
So, present age of Rakib = X + 12
And, present age of Babu = 2X + 12

As per question;
(2X + 12)/(X + 12) = 4/3
⇒ 6X + 36 = 4X + 48
⇒ 2X = 12
∴ X = 6

Present age of Rakib = 6 + 12 = 18 years
Present age of Babu = 2 × 6 + 12= 24 years

Required difference between their ages = 24 - 18 = 6 years

৪৫০.

Asif 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?

ক
3 years
খ
4 years
গ
6 years
ঘ
9 years

ব্যাখ্যা

Question: Asif 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, Asif'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

Asif'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.

৪৫১.

Rifat is twice as old as his friend Sifat. Sifat is 5 years older than Rafi. In 5 years, Rifat will be three times as old as Rafi. How old is Sifat now?

ক
10 years
খ
15 years
গ
5 years
ঘ
12 years

ব্যাখ্যা

Question: Rifat is twice as old as his friend Sifat. Sifat is 5 years older than Rafi. In 5 years, Rifat will be three times as old as Rafi. How old is Sifat now?

Solution:
Let
Rifat’s age = R
Sifat’s age = S
Rafi’s age = F

Now,
Rifat is twice as old as Sifat
∴ R = 2S
Sifat is 5 years older than Rafi
S = F + 5
∴ F = S - 5

In 5 years, Rifat will be three times as old as Rafi.
That means after 5 years,
R + 5 = 3(F + 5)
⇒ 2S + 5 = 3(S - 5 + 5)
⇒ 2S + 5 = 3S
∴ S = 5

So Sifat is 5 years old now.

৪৫২.

x years ago, Apu was one fifth as old as Topu. In x years, Topu will be twice as old as Apu. What is the ratio of Apu's current age to Topu's current age?

ক
2 : 5
খ
5 : 7
গ
3 : 7
ঘ
5 : 13
ঙ
None

ব্যাখ্যা

Question: x years ago, Apu was one fifth as old as Topu. In x years, Topu will be twice as old as Apu. What is the ratio of Apu's current age to Topu's current age?

Solution:
Let current age of Apu = c and Topu = a

ATQ,
(c - x)/(t - x) = 1/5
⇒ 5c - 5x = t - x
⇒ 5c - t = 4x .... (1)

and, (c + x)/(t + x) = 1/2
⇒ 2c + 2x = t + x
⇒ 2c - t = - x .... (2)

Now, (1)/(2) ⇒ (5c - t)/(2c - t) = 4x/-x
⇒ 8cx - 4tx = - 5cx + tx
⇒ 13cx = 5tx
⇒ 13c = 5t
⇒ c/t = 5/13
∴ c : t = 5 : 13

৪৫৩.

Four years ago, the father’s age was three times the age of his son. The total of the ages of the father and the son after four years will be 64 years. What is the father’s age at present?

ক
12 years
খ
36 years
গ
40 years
ঘ
44 years

ব্যাখ্যা

Question: Four years ago, the father’s age was three times the age of his son. The total of the ages of the father and the son after four years will be 64 years. What is the father’s age at present?

Solution:
let, age of son four years ago is x years old
age of father four years ago is 3x years old

after 4 years,
son's age = x + 4 + 4 = x + 8 years
father's age = 3x + 8 + 4 = 3x + 8 years

ATQ,
3x + 8 + (x + 8) = 64
⇒ 4x + 16 = 64
⇒ 4x = 48
⇒ x = 12

the father’s age at present is = 3 × 12 + 4 = 40 years

৪৫৪.

The sum of the ages of a mother and her daughter is 50 years. The mother’s age is four times the daughter’s age. After how many years will the mother’s age be three times the daughter’s age?

ক
10
খ
4
গ
5
ঘ
6

ব্যাখ্যা

Question: The sum of the ages of a mother and her daughter is 50 years. The mother’s age is four times the daughter’s age. After how many years will the mother’s age be three times the daughter’s age?

Solution:
Let the daughter's current age be x.
Then, the mother's current age is 4x.

ATC,
x + 4x = 50
⇒ 5x = 50
∴ x = 10

∴ Daughter's current age x = 10 years
and Mother's current age is 4x = 4 × 10 = 40 years

Let, the number of years after which mother’s age will be three times the daughter’s age be t.

So after t years,
The daughter’s age will be 10 + t
The mother’s age will be 40 + t

ATC,
40 + t = 3(10 + t)
⇒ 40 + t = 30 + 3t
⇒ 40 - 30 = 3t - t
⇒ 10 = 2t
⇒ t = 5

∴ After 5 years, the mother’s age will be three times the daughter’s age.

৪৫৫.

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?

ক
ক) 30
খ
খ) 35
গ
গ) 40
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’ units.
So, age of the person = (2x/5)
After 8 years, age of the person’s mother = ‘x + 8’ units.
So age of the person after 8 years = (2x/5) + 8
According to question:
(2x/5) + 8 = (a + 8)/2
=> (2x + 40)/5 = (a + 8)/2
=> 4a + 80 = 5a + 40
=>5a - 4a = 80 - 40
=> a = 40

So, the present age of his mother is 40 years.

৪৫৬.

The sum of the ages of A, B, and C is 120 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of A?

ক
ক) 30 years
খ
খ) 40 years
গ
গ) 50 years
ঘ
ঘ) 60 years

ব্যাখ্যা

Question: The sum of the ages of A, B, and C is 120 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of A?

Solution:
Let, A, B, and C's ages 10 years ago be 2x, 3x, and 4x years respectively

ATQ,
(2x + 10) + (3x + 10) + (4x + 10) = 120
⇒ 9x + 30 = 120
⇒ 9x = 90
⇒ x = 10

So, the age of A = 2 × 10 + 10 = 30

৪৫৭.

A father is 30 years older than his son. In 10 years, the father will be twice the son’s age. Find the present age of father.

ক
40
খ
45
গ
50
ঘ
55

ব্যাখ্যা

Question: A father is 30 years older than his son. In 10 years, the father will be twice the son’s age. Find the present age of father.

Solution:
Let the present age of the son be x years.
Then the present age of the father = x + 30 years.

In 10 years,
Son’s age = x + 10
Father’s age = x + 30 + 10 = x + 40

According to the problem, father’s age will be twice the son’s age,
x + 40 = 2(x + 10)
⇒ x + 40 = 2x + 20
⇒ 2x - x = 40 - 20
⇒ x = 20

∴ Present ages of father = x + 30 = 20 + 30 = 50

৪৫৮.

The present age of Kajol and Rohit are in the ratio of 7 : 8 respectively. After 6 years, the respective ratio between the age of Kajol and Rohit will be 9 : 10. What is the age of Rohit after 5 years?

ক
ক) 22 years
খ
খ) 24 years
গ
গ) 29 years
ঘ
ঘ) 34 years

ব্যাখ্যা

Let the present age of Kajol and Rohit is 7x and 8x respectively.
After 6 years, the age of Kajol = 7x + 6
After 6 years, the age of Rohit = 8x + 6
The ratio of age of Kajol and Rohit after 6 years is 9 : 10.
⇒ (7x + 6)/(8x + 6) = 9/10
⇒ 70x + 60 = 72x + 54
⇒ 2x = 6
⇒ x = 3

The age of Rohit after 5 years = 8 × 3 + 5 = 24 + 5 = 29 years

∴The age of Rohit after 5 years is 29 years.

৪৫৯.

A man is now 3 times as old as his son. In 10 years' time, the sum of their ages will be 76. How old was the man when his son was born?

ক
ক) 24 years
খ
খ) 42 years
গ
গ) 28 years
ঘ
ঘ) 32 years

ব্যাখ্যা

ধরি,
বর্তমানে পুত্রের বয়স = x বছর
পিতার বয়স 3x বছর

প্রশ্নমতে,
10 + x + 10 + 3x = 76
4x =76 - 20
4x =56
x=14
পুত্রের বয়স 14 বছর
পিতার বয়স = 3 × 14 = 42 বছর

জন্মের সময় পিতার বয়স ছিলো = 42 - 14 = 28 বছর

৪৬০.

The average of 18 observations was calculated and it was 124. Later on it was discovered that two observations 46 and 82 were incorrect. The correct values are 64 and 28. The correct average of 18 observations is -

ক
ক) 123
খ
খ) 137
গ
গ) 121
ঘ
ঘ) 122

ব্যাখ্যা

Sum of 18 observations = 18 x 124
=2232

Correct sum of 18 observations = 2232 - 46 - 82 + 64 + 28
= 2196
Therefore,
Correct average =2196/18
= 122.

৪৬১.

Daud is younger to Rohan by 9 years. If their ages are in the respective ratio of 4 : 5, how old is Daud?

ক
36 years
খ
23years
গ
29 years
ঘ
25 years
ঙ
Cannot be determined

ব্যাখ্যা

Question: Daud is younger to Rohan by 9 years. If their ages are in the respective ratio of 4 : 5, how old is Daud?

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

ATQ,
(x - 9)/x = 4/5
⇒ 5x - 45 = 4x
∴ x = 45

Hence, Daud's age = (x - 9) = 45 - 9 = 36 years.

৪৬২.

The sum of ages of 5 children born at the intervals of 4 years each is 70 years. What is the age of the eldest child?

ক
22 years
খ
24 years
গ
20 years
ঘ
18 years
ঙ
Nonr of these

ব্যাখ্যা

Question: The sum of ages of 5 children born at the intervals of 4 years each is 70 years. What is the age of the eldest child?

Solution:
Let the ages of children be x, (x + 4), (x + 8), (x + 12) and (x + 16) years.
Then,
x + (x + 4) + (x + 8) + (x + 12) + (x + 16) = 70
5x + 40 = 70
5x = 70 - 40
⇒ 5x = 30
⇒ x = 6
∴ Age of the eldest child = x + 16 = 6 + 16 = 22 years.

৪৬৩.

The ratio between the ages of Mobin and Xami is 4:5 and that between the ages of Mobin and Faisal is 5:6. If the sum of the ages of the three is 69 years, what is Xami’s age?

ক
ক) 20
খ
খ) 24
গ
গ) 25
ঘ
ঘ) 30

ব্যাখ্যা

Mobin's age:Xam's age = 4:5 = 1:5/4
Mobin's age:Faisal's age = 5:6 = 1:6/5
Let, Mobin's age be x years. Then, Xami's age = 5x/4
And, Faisal's age = 6x/5 years
∴ x + 5x/4 + 6x/5 = 69
⇒ 20x + 25x + 24x = 69 × 20
⇒ 20x + 25x + 24x = 1380
⇒ 69x = 1380
⇒ x = 1380/69
= 20
Xami's age = 5x/4 = (5 × 20)/4
= 25 years

৪৬৪.

One year ago, the ratio between Fahim and Rohan's ages was 3 : 2. One year hence, the ratio of their age will be 4 : 3. What is the sum of their present ages in years?

ক
12 years
খ
14 years
গ
18 years
ঘ
21 years
ঙ
16 years

ব্যাখ্যা

Question: One year ago, the ratio between Fahim and Rohan's ages was 3 : 2. One year hence, the ratio of their age will be 4 : 3. What is the sum of their present ages in years?

Solution:
ধরি, এক বছর আগে ফাহিমের বয়স ছিল 3x বছর এবং রোহানের বয়স ছিল 2x বছর।
বর্তমানে ফাহিমের বয়স = (3x + 1) বছর
বর্তমানে রোহানের বয়স = (2x + 1) বছর

এক বছর পর তাদের বয়সের অনুপাত হবে 4 : 3
∴ এক বছর পর ফাহিমের বয়স হবে = (3x + 1) + 1 = (3x + 2) বছর
∴ এক বছর পর রোহানের বয়স হবে = (2x + 1) + 1 = (2x + 2) বছর

প্রশ্নমতে,
(3x + 2)/(2x + 2) = 4/3
⇒ 3(3x + 2) = 4(2x + 2)
⇒ 9x + 6 = 8x + 8
⇒ 9x - 8x = 8 - 6
⇒ x = 2

সুতরাং, বর্তমানে ফাহিমের বয়স = (3 × 2) + 1 = 6 + 1 = 7 বছর
এবং বর্তমানে রোহানের বয়স = (2 × 2) + 1 = 4 + 1 = 5 বছর
∴ তাদের বর্তমান বয়সের যোগফল = 7 + 5 = 12 বছর।

৪৬৫.

The ages of five persons are 54, 82, 45, 55, and 59 years. What should be the age of a sixth person so that the average age becomes 61 years?

ক
65
খ
61
গ
75
ঘ
71

ব্যাখ্যা

Question: The ages of five persons are 54, 82, 45, 55, and 59 years. What should be the age of a sixth person so that the average age becomes 61 years?

Solution:
Let the age of the sixth person be x.
The average of six persons = Total age of 6 person/ 6

Accordingly:
(54 + 82 + 45 + 55 + 59 + x) / 6 = 61
⇒ (295 + x) / 6 = 61
⇒ 295 + x = 366
⇒ x = 366 - 295
⇒ x = 71

৪৬৬.

A father's age was 5 times his son's age 5 years ago and will be 3 times son's age after 2 years. The ratio of their present ages is -

ক
ক) 5 : 2
খ
খ) 5 : 3
গ
গ) 10 : 3
ঘ
ঘ) 11 : 5

ব্যাখ্যা

Question: A father's age was 5 times his son's age 5 years ago and will be 3 times son's age after 2 years. The ratio of their present ages is -

Solution:
ধরি,
৫ বছর আগে, পুত্রের বয়স x বছর
পিতার বয়স 5x বছর

বর্তমানে, পুত্রের বয়স x + 5 বছর
পিতার বয়স (5x + 5) বছর

২ বছর পর, পুত্রের বয়স x + 5 + 2 বছর
= x + 7 বছর

২ বছর পর পিতার বয়স = 5x + 5 + 2
= 5x + 7 বছর

প্রশ্নমতে,
5x + 7 = 3 (x + 7)
⇒ 5x + 7 = 3x + 21
⇒ 5x - 3x = 21 - 7
⇒ 2x = 14
∴ x = 7

পুত্রের বর্তমান বয়স = 7 + 5
= 12 বছর
পিতার বর্তমান বয়স = 5 × 7 + 5
= 35 + 5
= 40 বছর

∴ তাদের বর্তমান বয়সের অনুপাত = 40 : 12
= 10 : 3

৪৬৭.

The sum of Moni and Mimi's ages is 50 years and the difference between their ages is 6 years. What is the product of their ages?

ক
ক) 524 years
খ
খ) 616 years
গ
গ) 480 years
ঘ
ঘ) 300 years

ব্যাখ্যা

Question: The sum of Moni and Mimi's ages is 50 years and the difference between their ages is 6 years. What is the product of their ages?

Solution:
Let, Moni's age be = x years
and Mimi's age be = y years

ATQ,
x + y = 50.........(i)
x - y = 6.............(ii)

Now,
(i) + (ii),
x + y + x - y = 50 + 6
⇒ 2x = 56
⇒ x = 28

So, y = 50 - 28 = 22

∴ product of their ages = 28 × 22 = 616 years

৪৬৮.

The total ages of father and son is 42 years and the difference of thier ages is 22 years. What is son's age now?

ক
ক) 10 years
খ
খ) 11 years
গ
গ) 12 years
ঘ
ঘ) 13 years
ঙ
ঙ) 14 years

ব্যাখ্যা

Let's father's age x and son's age is y
ATQ, x + y = 42 ....(i)
x - y = 22 .... (ii)
(i) - (ii) = 2y = 20
∴ y = 10
∴ son's age is 10 years

৪৬৯.

Eight years ago, Karim was five times as old as his son. Now, Karim is 28 years older than his son. What is the present age of the son?

ক
16 years
খ
17 years
গ
18 years
ঘ
15 years
ঙ
14 years

ব্যাখ্যা

Question: Eight years ago, Karim was five times as old as his son. Now, Karim is 28 years older than his son. What is the present age of the son?

Solution:
ধরি,
বর্তমানে Karim-এর বয়স = x বছর এবং তার ছেলের বয়স = y বছর

৮ বছর আগে, Karim তার ছেলের বয়সের পাঁচ গুণ ছিল। অর্থাৎ
⇒ x - 8 = 5(y - 8).......... (১)

আবার,
বর্তমানে Karim তার ছেলের চেয়ে ২৮ বছর বড়।
x = y + 28

x এর মান (১) এ বসিয়ে পাই,
⇒ (y + 28) - 8 = 5(y - 8)
⇒ y + 20 = 5y - 40
⇒ 20 + 40 = 5y - y
⇒ 60 = 4y
∴ y = 15

∴ ছেলের বর্তমান বয়স = 15 বছর।

৪৭০.

The present age of the 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 son?

ক
ক) 20 years
খ
খ) 18 years
গ
গ) 36 years
ঘ
ঘ) 40 years

ব্যাখ্যা

Question: The present age of the 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 son?

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

ATQ,
2x - 10 = 3(x - 10)
⇒ 2x - 10 = 3x - 30
⇒ x = 20

৪৭১.

A’s age after 15 years would be equal to 5 times his age 5 years ago. Find his age 3 years hence.

ক
10 years
খ
13 years
গ
15 years
ঘ
17 years

ব্যাখ্যা

Question: A’s age after 15 years would be equal to 5 times his age 5 years ago. Find his age 3 years hence.

Solution:
Let A’s present age be ‘n’ years.
According to the question,
n + 15 = 5(n - 5)
⇒ n + 15 = 5 n – 25
⇒ 4n = 40
⇒ n = 10

∴ A’s present age = 10 years
Therefore, A’s age 3 years hence = 10 + 3 = 13 years

৪৭২.

If Mario was 32 years old 8 years ago, how old was he x years ago?

ক
ক) X-40
খ
খ) X-24
গ
গ) 40-x
ঘ
ঘ) 24-x

ব্যাখ্যা

Mario was 32 years old 8 years ago
Therefore, Mario's present age = 32 + 8 = 40 years
x years ago, his age = (40 - x) years

৪৭৩.

Today is Karim's 18th birthday and his father's 48th birthday. How many years from today will Karim's father be twice as old as Karim at that time?

ক
12 years
খ
15 years
গ
10 years
ঘ
16 years

ব্যাখ্যা

Question: Today is Karim's 18th birthday and his father's 48th birthday. How many years from today will Karim's father be twice as old as Karim at that time?

Solution:
Given that, Today Karim is 18 years old
And his Father is 48 years old
Age difference = 48 - 18 = 30 years (constant)

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

Now, Karim's age after x years = 18 + x
Father's age after x years = 48 + x

ATQ,
48 + x = 2(18 + x)
⇒ 48 + x = 36 + 2x
⇒ 2x - x = 48 - 36
⇒ x = 12

So, in 12 years, Karim's father will be twice as old as Karim.

৪৭৪.

Find the mother age after 8 years, if the ratio of age of mother and son is 5 ∶ 2 and the product of their ages in years is 1000.

ক
52 years
খ
58 years
গ
42 years
ঘ
None of these

ব্যাখ্যা

Question: Find the mother age after 8 years, if the ratio of age of mother and son is 5 ∶ 2 and the product of their ages in years is 1000.

Solution:
Given that,
Mother : Son = 5 ∶ 2
Product of ages = 1000

Let ages of mother and son be 5x, 2x

According to problem,
5x × 2x = 1000
⇒ 10x² = 1000
⇒ x² = 100 = 10²
∴ x = 10

So, age of mother after 8 years = (5x + 8)
= (5 × 10 + 8)
= 50 + 8
= 58 years

∴ The mother age is 58 years.

৪৭৫.

Hasan is two years older than Halim, who is twice as old as Habib. If the total of ages of Hasan, Halim, and Habib is 72, how old is Hasan?

ক
30 years
খ
32 years
গ
28 years
ঘ
34 years

ব্যাখ্যা

Question: Hasan is two years older than Halim, who is twice as old as Habib. If the total of ages of Hasan, Halim, and Habib is 72, how old is Hasan?

Solution:
Let,
Habib's age be = a years
Then, Halim's age = 2a years
Hasan's age = (2a + 2) years

ATQ,
(2a + 2) + 2a + a = 72
⇒ 5a = 70
∴ a = 14

Hence, Hasan's age = (2 × 14) + 2 = 30 years.

৪৭৬.

Trisha’s grandfather was 8 times older to her 16 years ago. He would be 3 times her age 8 years from now. Eight years ago, what was the ratio of Trisha’s age to that of her grandfather?

ক
3 : 8
খ
1 : 2
গ
1 : 5
ঘ
None of these

ব্যাখ্যা

Question: Trisha’s grandfather was 8 times older to her 16 years ago. He would be 3 times her age 8 years from now. Eight years ago, what was the ratio of Trisha’s age to that of her grandfather?

Solution:
Let, trisha was x years old 16 years ago.

grandfather was 8x years

ATQ,
8x + 16 + 8 = 3 (x + 16 + 8)
⇒ 8x + 24 = 3x + 72
⇒ 8x - 3x = 72 - 24 = 48
⇒ x = 48/5 = 9.6

Eight years ago, trisha was 9.6 + 8 = 17.6
grandfather was = 8 × 9.6 + 8 = 84.8

ratio = 17.6 : 84.8
= 176 : 848
= 11 : 53

৪৭৭.

The daughter's age is mean proportional to age of the father and son. The age of the father and son is 50 years and 8 years respectively. What is the age of the daughter?

ক
ক) 10 years
খ
খ) 16 years
গ
গ) 20 years
ঘ
ঘ) None of these

ব্যাখ্যা

Question: The daughter's age is mean proportional to age of the father and son. The age of the father and son is 50 years and 8 years respectively. What is the age of the daughter?

Solution:
Let,
1st proportional = Father's age
and 3rd proportional = Son's age

We know,
Mean Proportional = √(1st proportional × 3rd proportional)

So, daughter's age = √(50 × 8) years
= √400 years
= 20 years

৪৭৮.

A is two year older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B?

ক
ক) 10 years
খ
খ) 11 years
গ
গ) 12 years
ঘ
ঘ) 13 years

ব্যাখ্যা

Let C's age be x year.
Then, B's age = 2x year.
A's age = (2x + 2) year.
(2x + 2) + 2x + x = 27
5x = 25
=> x = 5
Hence, B's age = 2x = 10 year.

৪৭৯.

A father is twice as old as his daughter. If 20 years ago, the age of the father was 10 times the age of the daughter, what is the present age of the father?

ক
25 years
খ
30 years
গ
38 years
ঘ
45 years

ব্যাখ্যা

Question: A father is twice as old as his daughter. If 20 years ago, the age of the father was 10 times the age of the daughter, what is the present age of the father?

Solution:
Let, the present age of the father be 2x
So, the present age of the daughter = x

ATQ,
2x - 20 = 10(x - 20)
⇒ 2x - 20 = 10x - 200
⇒ 10x - 2x = 200 - 20
⇒ 8x = 180
⇒ x = 180/8
∴ x = 22.5

∴ The present age of father = 22.5 × 2 = 45 years

৪৮০.

The present ages of the three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

ক
16, 20, 28
খ
14, 24, 36
গ
16, 28, 36
ঘ
20, 36, 48

ব্যাখ্যা

Question: The present ages of the three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years).

Solution:

Let their present ages be 4x, 7x and 9x years respectively.

Then, (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.

৪৮১.

The present age of Mr. Rakib is three times the age of his son. Six years hence, the ratio of their ages will be 5 : 2. What is the present age of Mr. Rakib?

ক
ক) 48 years
খ
খ) 50 years
গ
গ) 52 years
ঘ
ঘ) 54 years

ব্যাখ্যা

Question: The present age of Mr. Rakib is three times the age of his son. Six years hence, the ratio of their ages will be 5 : 2. What is the present age of Mr. Rakib?

Solution:
Let the age of son is X years
so, Mr. Rakib's age is 3X years

ATQ,
(3X + 6) : (X + 6) = 5 : 2
5X + 30 = 6X + 12
X = 18

Hence, the present age of Mr. Rakib = (3 × 18) = 54 years.

৪৮২.

Kamal was 4 times as old as his son 8 years ago. After 8 years, Kamal will be twice as old as his son. Find out the present age of Kamal.

ক
42 years
খ
38 years
গ
36 years
ঘ
40 years

ব্যাখ্যা

Let the age of the son before 8 years ago = x
Then, age of Kamal before 8 years age = 4x
After 8 years, Kamal will be twice as old as his son
(4x + 16) = 2(x + 16)
⇒ 4x - 2x = 32 - 16
⇒ 2x = 16
⇒ x = 8 years.
The present age of kamal = 4x + 8
= (4 × 8) + 8
= 32 + 8
= 40 years.

৪৮৩.

The difference between the present ages of Amit and Robin is 8 years. Four years ago, the ratio of their ages was 3 : 4 respectively. What is Robin's present age?

ক
28 years
খ
30 years
গ
36 years
ঘ
42 years

ব্যাখ্যা

Question: The difference between the present ages of Amit and Robin is 8 years. Four years ago, the ratio of their ages was 3 : 4 respectively. What is Robin's present age?

Solution:
Let, 4 years ago,
Amit's age was = 3x
Robin's age = 4x

ATQ,
(4x + 4) - (3x + 4) = 8
⇒ 4x + 4 - 3x - 4 = 8
∴ x = 8

Robin's present age = (4 × 8) + 4 = 36 years

৪৮৪.

What is Rasel's present age, if after 20 years his age will be 10 times his age 10 years back?

ক
6.2 years
খ
7.7 years
গ
10 years
ঘ
13.3 years
ঙ
None of these

ব্যাখ্যা

Question: What is Rasel's present age, if after 20 years his age will be 10 times his age 10 years back?

Solution:

Let Rasel's present age be x

Rasel's age before 10 years = x - 10)

Rasel's age after 20 years = (x + 20)

We are given that,
Rasel's age after 20 years (x + 20) is 10 times his age 10 years back (x - 10)

Therefore,
(x + 20) = 10(x - 10)

⇒ x + 20 = 10x - 100

⇒ 9x = 120
∴ x = 13.3 years

৪৮৫.

If Mario was 32 years old 8 years ago, how old was he x years ago?

ক
x - 40
খ
x - 24
গ
40 - x
ঘ
24 - x
ঙ
24 + x

ব্যাখ্যা

Question: If Mario was 32 years old 8 years ago, how old was he x years ago?

Solution:
If Mario's current age is M,
then Mario's age 8 years ago = M - 8;
Here,
M - 8 = 32;
therefore, M = 40 (Mario's current age)

∴ His age x years ago means M - x or 40 - x;

৪৮৬.

Rifat got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. What is the present age of Rifat?

ক
ক) 32 years
খ
খ) 40 years
গ
গ) 48 years
ঘ
ঘ) 42 years

ব্যাখ্যা

Question: Rifat got married 8 years ago. His present age is 6/5 times his age at the time of his marriage. What is the present age of Rifat?
Solution:
Let, Rifatj's age 8 years ago be x years
His present age is = x + 8 years

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

His present age is = 40 + 8 = 48 years

৪৮৭.

The present ages of Kamal and Jamal are in the ratio 5 : 7. After 8 years, the ratio of their ages will be 3 : 4. What is the difference in their present ages?

ক
12 years
খ
14 years
গ
16 years
ঘ
18 years

ব্যাখ্যা

Question: The present ages of Kamal and Jamal are in the ratio 5 : 7. After 8 years, the ratio of their ages will be 3 : 4. What is the difference in their present ages?

Solution:
Let their present ages be 5x and 7x.

After 8 years, Kamal's age = 5x + 8
Jamal's age = 7x + 8

According to the question,
(5x + 8)/(7x + 8) = 3/4
⇒ 4(5x + 8) = 3(7x + 8)
⇒ 20x + 32 = 21x + 24
⇒ 20x - 21x = 24 - 32
⇒ - x = - 8
∴ x = 8

∴ Kamal's present age = 5 × 8 = 40 years
∴ Jamal's present age = 7 × 8 = 56 years

∴ Difference = 56 - 40 = 16 years

৪৮৮.

The ages of Rima and Bina are in the ratio 9 : 8 respectively. After 5 years, the ratio of their ages will be 10 : 9. What is the difference in their ages?

ক
10 years
খ
7 years
গ
3 years
ঘ
5 years

ব্যাখ্যা

Question: The ages of Rima and Bina are in the ratio 9 : 8 respectively. After 5 years, the ratio of their ages will be 10 : 9. What is the difference in their ages?

Solution:
Let Rima’s age be = 9x years.
Then Bina’s age = 8x years

According to the question,
(9x + 5)/(8x + 5) = 10/9
⇒ 9(9x + 5) = 10(8x + 5)
⇒ 81x + 45 = 80x + 40
⇒ 81x - 80x = 40 - 45
⇒ - x = - 5
∴ x = 5

∴ The difference in their ages = 9x - 8x = x = 5 years.

৪৮৯.

Age of a mother 10 years ago was 3 times the age of her son. After 10 years, the mother's age will be twice that of his son. Find the ratio of their present ages?

ক
ক) 11 : 7
খ
খ) 9 : 5
গ
গ) 7 : 4
ঘ
ঘ) 7 : 3

ব্যাখ্যা

We are given that,
age of mother 10 years ago was 3 times the age of her son
So,
let the age of the son be x and as the mother's age is 3 times the age of her son, let it be 3x, three years ago.
At present,
Mother's age will be (3x + 10) and son's age will be (x + 10)
After 10 years,
Mother's age will be (3x + 10) +10 and son’s age will be (x + 10) + 10

Mother's age is twice that of son
(3x + 10) +10 = 2 [(x + 10) + 10]
(3x + 20) = 2[x + 20]
Solving the equation, we get x = 20
We are asked to find the present ratio.
(3x + 10) : (x + 10) = 70 : 30
(3x + 10) : (x + 10) = 7 : 3.

৪৯০.

8 years ago, the ratio of A’s age to B’s age was 4:5. At present the ratio of B’s age to C’s age is 4:5. At present, the difference between A’s age and C’s age is 30 years, then what is the sum of the ages of A, B and c?

ক
ক) 138 years
খ
খ) 160 years
গ
গ) 148 years
ঘ
ঘ) 152 years
ঙ
ঙ) 164 years

ব্যাখ্যা

Let, 8 years ago,
the age of A and B was 4x and 5x respectively. Age of C = y
so, the present age of A and B is 4x + 8 and 5x + 8 respectively

A/Q,
5x + 8 : y = 4 : 5 ------------ (1)
y - (4x + 8) = 20 ----------- (2)
Solving this equation we will get x = 8 and y = 60

So, present age of Age of A = 4×8 + 8
= 40
and present age of B = 5×8 + 8
= 48
From equation (1),
C = {(5x + 8) × 5} ÷ 4 = 60

So, the total age of A, B & C= 40 + 48 + 60
= 148

৪৯১.

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 38 years now, the son's age six years back was:

ক
13 years
খ
24 years
গ
34 years
ঘ
None of these

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 38 years now, the son's age five years back was:

Solution:

Let, at present son is x years old

so, at the time of his birth, the father was x years old

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

= 2x years

Now,

2x = 38

⇒ x = 38/2

∴ x = 19 years

∴ The son's age five years back was = 19 - 6

= 13 years

৪৯২.

The sum of the ages of a man and his son is 70 years. After 10 years, the ratio of their ages will be 2 : 1. What is the son's present age?

ক
16
খ
22
গ
20
ঘ
None of these

ব্যাখ্যা

Question: The sum of the ages of a man and his son is 70 years. After 10 years, the ratio of their ages will be 2 : 1. What is the son's present age?

Solution:
ধরি,
বাবার বর্তমান বয়স x বছর
ছেলের বর্তমান বয়স y বছর

প্রশ্নমতে,
x + y = 70 ............ (1)

আবার, 10 বছর পর,
(x + 10)/(y + 10) = 2/1
⇒ x + 10 = 2(y + 10)
⇒ x + 10 = 2y + 20
⇒ x - 2y = 10 ............. (2)

Equation, (1) - (2)
x + y - x + 2y = 70 - 10
⇒ 3y = 60
⇒ y = 20

∴ পুত্রের বর্তমান বয়স = 20 বছর

৪৯৩.

Age of Kamal will be 4 times the age of Rina in 6 years from today. If ages of Kamal and Mahi are 7 times and 6 times the age of Rina respectively, what is present age of Kamal?

ক
38 years
খ
52 years
গ
48 years
ঘ
36 years
ঙ
42 years

ব্যাখ্যা

Question: Age of Kamal will be 4 times the age of Rina in 6 years from today. If ages of Kamal and Mahi are 7 times and 6 times the age of Rina respectively, what is present age of Kamal?

Solution:
Let,
Rina's present age = R years
Then,
Kamal's present age = 7 × R = 7R
Mahi's present age = 6 × R = 6R

Age of Kamal will be 4 times the age of Rina in 6 years.
Kamal’s age after 6 years = 7R +6
Rina’s age after 6 years = R + 6

ATQ,
7R + 6 = 4(R + 6)
⇒ 7R + 6 = 4R + 24
⇒ 7R - 4R = 18
⇒ R = 18/3
∴ R = 6

∴ Kamal's present age = 7 × R = 7R = 7 × 6 = 42 years

৪৯৪.

Father is aged four times more than his son. After 8 years, he would be two and a half times of son's age. What is the current age of the father?

ক
ক) 30 years
খ
খ) 22 years
গ
গ) 40 years
ঘ
ঘ) 32 years

ব্যাখ্যা

Question: Father is aged four times more than his son. After 8 years, he would be two and a half times of son's age. What is the current age of the father?

Solution:
Let,
The current age of son is x years
∴ The current age of the father is 4x years

ATQ,
4x + 8 = (5/2)(x + 8)
⇒ 8x + 16 = 5x + 40
⇒ 3x = 24
∴ x = 8

∴ The current age of the father is (4 × 8) years
= 32 years

৪৯৫.

Eight year ago, Shanta's age was equal to the sum of the present ages of her one son and one daughter. Five years hence, the respective ratio between the ages of her daughter and her son that time will be 7 : 6. If Shanta's husband is 7 years elder to her and his present age is three times the present age of their son, what is the present age of the daughter ? (in year)

ক
18 years
খ
20 years
গ
23 years
ঘ
25 years

ব্যাখ্যা

Question: Eight year ago, Shanta's age was equal to the sum of the present ages of her one son and one daughter. Five years hence, the respective ratio between the ages of her daughter and her son that time will be 7 : 6. If Shanta's husband is 7 years elder to her and his present age is three times the present age of their son, what is the present age of the daughter ? (in year)

Solution:
Let, the age of the son and the daughter of Shanta be 6a years and 7a years respectively.
5 years hence, present age of son = (6a - 5)
and present age of daughter = (7a - 5)

Eight years ago, the age of Shanta = (6a - 5 + 7a - 5) = 13a - 10
So, present age of Shanta = (13a - 10 + 8) = 13a - 2
Since, present age of Shanta's husband = 3(6a - 5)

The difference of present age of Shanta's husband and Shanta = 7 (Given)

ATQ,
3(6a - 5) - (13a - 2) = 7
⇒ 18a - 15 - 13a + 2 = 7
⇒ 5a = 20

∴ The present age of daughter = (7a - 5)
= 7 × 4 - 5
= 23 years

৪৯৬.

The sum of the ages of the son and father is 120 years. The father age is 3 times than the son. What is the age of father?

ক
ক) 75
খ
খ) 80
গ
গ) 90
ঘ
ঘ) 85

ব্যাখ্যা

ধরি,
পুত্রের বয়স x বছর
পিতার বয়স 3x
প্রশ্নমতে,
x + 3x = 120
4x = 120
x=30

পিতার বয়স = 3 × 30 = 90 বছর

৪৯৭.

The sum of the ages of X, Y, and Z is 120 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Y?

ক
30 years
খ
40 years
গ
50 years
ঘ
45 years

ব্যাখ্যা

Question: The sum of the ages of X, Y, and Z is 120 years. Ten years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Y?

Solution:
Let, X, Y, and Z's ages 10 years ago be 2a, 3a, and 4a years respectively

ATQ,
(2a + 10) + (3a + 10) + (4a + 10) = 120
⇒ 9a + 30 = 120
⇒ 9a = 90
∴ a = 10

So, the age of Y = 3 × 10 + 10 = 40 years.

৪৯৮.

Rina is currently four times older than Meena. Six years ago, Rina was ten times older than Meena. What will be the sum of their ages after 5 years?

ক
45
খ
61
গ
75
ঘ
55

ব্যাখ্যা

Question: Rina is currently four times older than Meena. Six years ago, Rina was ten times older than Meena. What will be the sum of their ages after 5 years?

Solution:
ধরি,
বর্তমানে মিনার বয়স = x বছর
∴ রিনার বয়স = 4x বছর

৬ বছর পূর্বে,
মিনার বয়স (x - 6) বছর.
রিনার বয়স (4x - 6) বছর.

ATC,
4x - 6 = 10(x - 6)
⇒ 4x - 6 = 10x - 60
⇒ 6x = 54
∴ x = 9

∴ মিনার বর্তমান বয়স = 9 বছর
রিনার বর্তমান বয়স = 4 × 9 = 36 বছর

5 বছর পরে,
মিনার বয়স = 9 + 5 = 14 বছর
রিনার বয়স = 36 + 5 = 41 বছর

∴5 বছর পরে উভয়ের বয়সের যোগফল = 14 + 41 = 55 বছর

৪৯৯.

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 husband is:

ক
35
খ
40
গ
50
ঘ
None

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.

৫০০.

A man is 26 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

ক
24 years
খ
22 years
গ
20 years
ঘ
30 years

ব্যাখ্যা

Question: A man is 26 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is:

Solution:
Let the son's present age be x years.
Then, the man's present age = (x + 26) years.

∴ (x + 26) + 2 = 2(x + 2)

⇒ x + 28 = 2x + 4

⇒ x = 24

∴ The present age of his son = 24 years.