Problems on Ages

PrepBank · পাতা ২ / ৭ · ১০১–২০০ / ৬০৭

১০১.

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. How old is the mother at present?

ক
ক) 40 years
খ
খ) 45 years
গ
গ) 52 years
ঘ
ঘ) None of these

সঠিক উত্তর: ক

ক) 40 years

উত্তর

সঠিক উত্তর: ক

ক) 40 years

ক

ব্যাখ্যা

Suppose, mother's present age is x years
Therefore, person's present age = 2x/5 years
(x + 8)/2 = 2x/5 + 8
⇒ (x + 8)/2 = (2x + 40)/5
⇒ 5x + 40 = 4x + 80
⇒ x = 40 years

১০২.

Sum of present ages of A, B and C is 92 years. If 4 years ago, the ratio of their ages were 1 : 2 : 3 respectively, find A’s present age.

ক
18.5 year
খ
17.3 years
গ
14.8 years
ঘ
20.3 years

সঠিক উত্তর: খ

17.3 years

উত্তর

সঠিক উত্তর: খ

17.3 years

খ

ব্যাখ্যা

Question: Sum of present ages of A, B and C is 92 years. If 4 years ago, the ratio of their ages were 1 : 2 : 3 respectively, find A’s present age.

Solution:
Sum of present ages of A, B and C is = 92 years
Therefore , Sum of their ages 4 years ago = 92 - (4 × 3) = 92 - 12 = 80 years.

4 years ago ratio of the ages of A , B and C was = 1 : 2 : 3

Therefore, A’s age four years ago = (1/6) × 80 years = 13.3 years.
∴ A’s present age = 13.3 + 4 = 17.3 years

১০৩.

The present ages of P and Q are in the ratio 2 : 7. After 8 years, the ratio of their ages will be 3 : 8. What is the difference in their present ages?

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

সঠিক উত্তর: ঘ

40 years

উত্তর

সঠিক উত্তর: ঘ

40 years

ঘ

ব্যাখ্যা

Question: The present ages of P and Q are in the ratio 2 : 7. After 8 years, the ratio of their ages will be 3 : 8. What is the difference in their present ages?

Solution:
Let the present ages be,
P = 2x and Q = 7x

Ages after 8 years,
P = 2x + 8, Q = 7x + 8

According to the problem, the ratio becomes 3:8
(2x + 8)/(7x + 8) = 3/8
⇒ 8(2x + 8) = 3(7x + 8)
⇒ 16x + 64 = 21x + 24
⇒ 64 - 24 = 21x - 16x
⇒ 40 = 5x
⇒ x = 8

P = 2 × 8 = 16 years
Q = 7 × 8 = 56 years

∴ Difference = 56 - 16 = 40 years

১০৪.

The ratio of Rifat and Rafat's ages is 4 : 3. Rifat will be 30 years old after 6 years. How old is Rafat now?

ক
ক) 12 years
খ
খ) 15 years
গ
গ) 18 years
ঘ
ঘ) 24 years

সঠিক উত্তর: গ

গ) 18 years

উত্তর

সঠিক উত্তর: গ

গ) 18 years

গ

ব্যাখ্যা

Question: The ratio of Rifat and Rafat's ages is 4 : 3. Rifat will be 30 years old after 6 years. How old is Rafat now?

Solution:
Let, Rifat's age is = 4x years
and Rafat's age is = 3x years

ATQ,
4x + 6 = 30
⇒ 4x = 24
⇒ x = 6

So, Rafat's age is = (3 ×6) = 18 years

১০৫.

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 ?

ক
ক) 23
খ
খ) 24
গ
গ) 25
ঘ
ঘ) None

সঠিক উত্তর: ক

ক) 23

উত্তর

সঠিক উত্তর: ক

ক) 23

ক

ব্যাখ্যা

Question: 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 ?

Solution:
Let the average age of the whole team by x years

Now
∴ 11x - (26 + 29) = 9(x - 1)
⇒ 11x - 9x = 46
⇒ 2x = 46
⇒ x = 23

Average age of the team is 23 years

১০৬.

Rahim is currently four times as old as Kabir. Five years ago, Rahim was seven times as old as Kabir. What will be the sum of their ages after 12 years?

ক
74
খ
60
গ
66
ঘ
78

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: Rahim is currently four times as old as Kabir. Five years ago, Rahim was seven times as old as Kabir. What will be the sum of their ages after 12 years?

Solution:
Let Kabir's current age = x years
Rahim's current age = 4x years

5 years ago:
Rahim's age = 4x - 5
Kabir's age = x - 5

According to the question,
4x - 5 = 7(x - 5)
⇒ 4x - 5 = 7x - 35
⇒ - 5 + 35 = 7x - 4x
⇒ 30 = 3x
∴ x = 10

So, Kabir's age = 10 years, Rahim's age = 4 × 10 = 40 years

After 12 years:
Kabir's age: 10 + 12 = 22
Rahim's age: 40 + 12 = 52

∴ Sum: 22 + 52 = 74

১০৭.

A mother said to her daughter "I was as old as you are at present at the time of your birth". If the mother's age is 40 years now, the daughter's age five years back was-

ক
20 years
খ
18 years
গ
15 years
ঘ
35 years

সঠিক উত্তর: গ

15 years

উত্তর

সঠিক উত্তর: গ

15 years

গ

ব্যাখ্যা

Question: A mother said to her daughter "I was as old as you are at present at the time of your birth". If the mother's age is 40 years now, the daughter's age five years back was-

Solution:
ধরি,
মেয়ের বর্তমান বয়স = x বছর।
মাতার বর্তমান বয়স (x + x) = 2x বছর

শর্তমতে,
2x = 40
x = 20

∴ 5 বছর পূর্বে মেয়ের বয়স ছিল = (20 - 5) বছর
= 15 বছর

১০৮.

The sum of the present ages of A and B is 50. After 2 years B’s age will be 2 years more than that of C. If A is younger than C by 4 years, find the age of B 8 years ago

ক
20
খ
18
গ
22
ঘ
14
ঙ
16

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Present age of A + B = 50
A + 4 = C
So, A = C - 4
B = C + 2

Now,
C + 2 + C - 4 = 50
Or, 2C = 52
Or, C = 26

So,
B = 26 + 2
= 28
8 years Ago B age = (28 - 8) = 20 years

১০৯.

A couple has a son and a daughter. The age of the father is four times the son and the age of the mother is three times the daughter. The mother is 6 years younger to the father and the daughter is 3 years older than the son. What is the age of the mother?

ক
52 years
খ
54 years
গ
56 years
ঘ
50 years

সঠিক উত্তর: খ

54 years

উত্তর

সঠিক উত্তর: খ

54 years

খ

ব্যাখ্যা

Question: A couple has a son and a daughter. The age of the father is four times the son and the age of the mother is three times the daughter. The mother is 6 years younger to the father and the daughter is 3 years older than the son. What is the age of the mother?

Solution:
Let, father, mother, son and daughter have age of F, M, S and D respectively.
ATQ,
F = 4S ………….(i)
M = 3D………….(ii)
M = F - 6………..(iii)
D = S + 3………..(iv)

From (ii) we get,
M = 3D
Or, M = 3(S + 3) [from (iv)]
Or, M = 3{(F/4) + 3} [from (i)]
Or, M = ¾(F + 12)
Or, M = ¾(M + 6 + 12) [from(iii)]
Or, M = ¾(M + 18)
Or, 4M = 3M + 54
Or, M = 54

∴ the age of the mother is 54 years.

১১০.

A man's age is 125 % of what it was 10 years ago, but 83 (1/3 )% of what it will be after 10 years. What is his present age?

ক
40
খ
60
গ
50
ঘ
70
ঙ
80

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

The age before 10 years increased by 25 % in 10 years.
In other words, the age before 10 years would have increased by 100 % in 40 years.
That is, the age before 10 years is 40 years. Therefore, the present age is 50.

১১১.

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?

ক
36
খ
35
গ
34
ঘ
33

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

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?

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

∴ Present age of man = 6X + 4 = 6 × 5 + 4 = 30 + 4 = 34 years

১১২.

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

ক
ক) 19
খ
খ) 39
গ
গ) 29
ঘ
ঘ) 49

সঠিক উত্তর: খ

খ) 39

উত্তর

সঠিক উত্তর: খ

খ) 39

খ

ব্যাখ্যা

ধরি
B এর বর্তমান বয়স = x বছর
A এর বর্তমান বয়স = x + 9 বছর

প্রশ্নমতে,
(x + 9) + 10 = 2(x - 10)
x + 19 = 2x - 20
2x - 20 = x + 19
2x - x = 19 + 20
x = 39
B এর বর্তমান বয়স = 39 বছর

১১৩.

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
11
খ
7
গ
9
ঘ
10
ঙ
8

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

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.

১১৪.

The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 4 times the father's age at that time. What are the present ages of the father and son?

ক
10, 40
খ
12, 45
গ
9, 36
ঘ
18, 64

সঠিক উত্তর: গ

9, 36

উত্তর

সঠিক উত্তর: গ

9, 36

গ

ব্যাখ্যা

Question: The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was 4 times the father's age at that time. What are the present ages of the father and son?

Solution:
ধরি,
বর্তমানে বাবার বয়স = x বছর
বর্তমানে ছেলের বয়স = (45 - x) বছর

5 বছর আগে,
বাবার বয়স = x - 5
ছেলের বয়স = (45 - x) - 5 = 40 - x

প্রশ্নমতে,
(x - 5)(40 - x) = 4(x - 5)
⇒ 40 - x = 4
⇒ x = 40 - 4 = 36

∴ বাবার বর্তমান বয়স = 36 বছর
ছেলের বর্তমান বয়স = 45 - 36 = 9 বছর

১১৫.

Ten year ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages

ক
ক) 15
খ
খ) 25
গ
গ) 35
ঘ
ঘ) 45

সঠিক উত্তর: গ

গ) 35

উত্তর

সঠিক উত্তর: গ

গ) 35

গ

ব্যাখ্যা

Let A's age 10 year ago = x year.
Then, B's age 10 year ago = 2x year.
(x + 10) / (2x+ 10) = 3/4
=> x = 5.
So, the total of their present ages
=(x + 10 + 2x + 10)
= (3x + 20)
= 35 year.

১১৬.

The ratio of the present ages of P and Q is 3 : 4. Five years ago, the ratio of their ages was 5 : 7. Find their present ages.

ক
30, 40
খ
24, 32
গ
27, 36
ঘ
40, 50

সঠিক উত্তর: ক

30, 40

উত্তর

সঠিক উত্তর: ক

30, 40

ক

ব্যাখ্যা

Question: The ratio of the present ages of P and Q is 3 : 4. Five years ago, the ratio of their ages was 5 : 7. Find their present ages.

Solution:
As the ratio of their present ages is 3 : 4 ,
let their present ages be 3x and 4x.
So, 5 years ago, as the ratio of their ages was 5 : 7,

According to the question,
(3x - 5) : (4x - 5) = 5 : 7
⇒ (3x - 5)/(4x - 5) = 5/7
⇒ 21x - 35 = 20x - 25
⇒ x = 10

Hence, their present ages are 3x = 30 and 4x = 40

১১৭.

A man'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 sum of their ages at present ages?

ক
ক) 40
খ
খ) 48
গ
গ) 52
ঘ
ঘ) 56

সঠিক উত্তর: ঘ

ঘ) 56

উত্তর

সঠিক উত্তর: ঘ

ঘ) 56

ঘ

ব্যাখ্যা

Question: A man'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 sum of their ages at present ages?

Solution:
Let, the mother's age be = x years
so, man's age = (2x/5) years

According to the question,
(2x/5) + 8 = (x + 8)/2
⇒ (2x + 40)/5 = (x + 8)/2
⇒ 5x + 40 = 4x + 80
⇒ x = 40

mother's age = 40 years
man's age = (2 × 40)/5 = 16 years

So, sum their age = 40 + 16 = 56 years

১১৮.

What is John's present age, if 10 years later his age will be 5 times his age 6 years ago?

ক
16.2 years
খ
7.7 years
গ
8.7 years
ঘ
10 years
ঙ
None of these

সঠিক উত্তর: ঘ

10 years

উত্তর

সঠিক উত্তর: ঘ

10 years

ঘ

ব্যাখ্যা

Question: What is John's present age, if 10 years later his age will be 5 times his age 6 years ago?

Solution:
Let John's present age be x
John's age 6 years ago = (x - 6)
John's age 10 years later = (x + 10)
We are given that John's age after 10 years (x + 10) is 5 times his age 6 years ago (x - 6).

Therefore,
(x +10) = 5(x - 6)
⇒ x + 10 = 5x - 30
⇒ 4x = 40
∴ x = 10

১১৯.

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

ক
ক) 7
খ
খ) 8
গ
গ) 9
ঘ
ঘ) 10

সঠিক উত্তর: ঘ

ঘ) 10

উত্তর

সঠিক উত্তর: ঘ

ঘ) 10

ঘ

ব্যাখ্যা

ধরি, C এর বয়স x বছর
তাহলে B এর বয়স = 2x বছর এবং A এর বয়স = (2x + 2) বছর
প্রশ্নমতে, x + 2x + 2x + 2 = 27
⇒ 5x = 27 - 2
⇒ x = 25/5
⇒ x = 5
∴ B এর বয়স (2×5) বছর = 10 বছর

১২০.

A man is 24 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
ক) 20
খ
খ) 21
গ
গ) 22
ঘ
ঘ) 23
ঙ
ঙ) 25

সঠিক উত্তর: গ

গ) 22

উত্তর

সঠিক উত্তর: গ

গ) 22

গ

ব্যাখ্যা

Let the son's present age be x years.
Then, man's present age = (x + 24) years
=> (x + 24) + 2 = 2(x + 2)
=> x + 26 = 2x + 4
So, x = 22

১২১.

The combined ages of 5 children, with each child 4 years older than the next, equal 70 years. How old is the oldest?

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

সঠিক উত্তর: গ

22 years

উত্তর

সঠিক উত্তর: গ

22 years

গ

ব্যাখ্যা

Question: The combined ages of 5 children, with each child 4 years older than the next, equal 70 years. How old is the oldest?

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.

১২২.

Nazma's age is 1/5 th of her father's age. Nazma's father's age will be twice of Moni's age after 10 years. If Moni's 8th birthday was celebrated 2 years ago,then what is Nazma's present age?

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

সঠিক উত্তর: খ

6 years

উত্তর

সঠিক উত্তর: খ

6 years

খ

ব্যাখ্যা

Question: Nazma's age is 1/5 th of her father's age. Nazma's father's age will be twice of Moni's age after 10 years. If Moni's 8th birthday was celebrated 2 years ago,then what is Nazma's present age?

Solution:
মণির বর্তমান বয়স = ৮ + ২ বছর
= ১০ বছর

১০ বছর পর, মণির বয়স = ১০ + ১০ বছর
= ২০ বছর

১০ বছর পর পিতার বয়স = ২০ × ২ বছর
= ৪০ বছর

বর্তমানে পিতার বয়স = ৪০ - ১০ বছর
= ৩০ বছর

নাজমার বর্তমান বয়স = ৩০/৫ বছর
= ৬ বছর

১২৩.

The average age of 12 children is 15 years. If another child comes the average age comes to 13. What is the age of the new child?

ক
11 years
খ
7 years
গ
9 years
ঘ
5 years

সঠিক উত্তর: ক

11 years

উত্তর

সঠিক উত্তর: ক

11 years

ক

ব্যাখ্যা

Question: The average age of 12 children is 15 years. If another child comes the average age comes to 13. What is the age of the new child?

Solution:
Sum of 12 children ages = 12 × 15 = 180
Sum of the 13 children ages = 13 × 13 = 169
So age of new children = 180 - 169
= 11

[বাস্তবিকভাবে নতুন একজনের বয়স যুক্ত হওয়ার পর বয়সের গড় কম-বেশি হতে পারে তবে ১২ জনের মোট বয়স (১৮০ বছর) অপেক্ষা ১৩ জনের মোট বয়স (১৬৯ বছর) কম হতে পারে না। এই প্রশ্নটি যেহেতু জব সল্যুশনের প্রশ্ন তাই গাণিতিক নিয়ম অনুযায়ী ১১ বছর উত্তর রাখা হয়েছে]

১২৪.

The ratio of the present ages of Rahim and Karim is 9 : 10 respectively. Twenty years ago, the ratio of their ages was 4 : 5 respectively. What is the present age of Rahim?

ক
34 years
খ
36 years
গ
42 years
ঘ
24 years

সঠিক উত্তর: খ

36 years

উত্তর

সঠিক উত্তর: খ

36 years

খ

ব্যাখ্যা

Question: The ratio of the present ages of Rahim and Karim is 9 : 10 respectively. Twenty years ago, the ratio of their ages was 4 : 5 respectively. What is the present age of Rahim?

Solution:
The ratio of the present ages of Rahim and Karim = 9 : 10
Let's consider the present ages of Rahim and Karim 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 Rahim = (9 × 4) years.
= 36 years.

১২৫.

The product of the ages of Minhaz and Rahul is 180. If twice the age of Rahul is more than Minhaz's age by 2 years, then find Rahul's age.

ক
ক) 10 years
খ
খ) 18 years
গ
গ) 20 years
ঘ
ঘ) 24 years

সঠিক উত্তর: ক

ক) 10 years

উত্তর

সঠিক উত্তর: ক

ক) 10 years

ক

ব্যাখ্যা

Question: The product of the ages of Minhaz and Rahul is 180. If twice the age of Rahul is more than Minhaz's age by 2 years, then find Rahul's age.

Solution:
Let Minhaz's age be x years
Then, Rahul's age = 180/x years

ATQ,
2 × (180/x = x + 2
⇒ (360/x) - x = 2
⇒ 360 - x² = 2x
⇒ x² + 2x - 360 = 0
⇒ x² + 20x - 18x - 360 = 0
⇒ x(x + 20) - 18(x + 20) = 0
⇒ (x - 18) (x + 20) = 0
∴ x = 18

So, Rahul's age is = 180/18 = 10 years

১২৬.

The sum of the ages of the father and son is 80 years. If ten years ago the age of father was three times that of his son, find the present age of the father.

ক
60 years
খ
45 years
গ
50 years
ঘ
55 years

সঠিক উত্তর: ঘ

55 years

উত্তর

সঠিক উত্তর: ঘ

55 years

ঘ

ব্যাখ্যা

Question: The sum of the ages of the father and son is 80 years. If ten years ago the age of father was three times that of his son, find the present age of the father.

Solution:
Let the age of son 10 years ago = x
The age of father 10 years ago = 3x

⇒ x + 10 + 3x + 10 = 80
⇒ 4x + 20 = 80
⇒ 4x = 60
⇒ x = 15

Son's present age = 15 + 10 = 25 years
∴ Present age of father = 3 × 15 + 10 = 45 + 10 = 55 years

১২৭.

A gentleman has two sons. The present age of the elder son is twice the present age of the younger son. Three years ago, the elder son’s age was three times the age of the younger son. Find the current age of the elder son.

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

সঠিক উত্তর: গ

12 years

উত্তর

সঠিক উত্তর: গ

12 years

গ

ব্যাখ্যা

Question: A gentleman has two sons. The present age of the elder son is twice the present age of the younger son. Three years ago, the elder son’s age was three times the age of the younger son. Find the current age of the elder son.

Solution:
ধরি,
ছোট ছেলের বয়স = x বছর
বড় ছেলের বয়স = 2x বছর

3 বছর পূর্বে,
ছোট ছেলের বয়স ছিলো = x - 3 বছর
বড় ছেলের বয়স ছিলো = 2x - 3 বছর

প্রশ্নমতে,
(2x - 3) = 3(x - 3)
বা, 2x - 3 = 3x - 9
বা, 3x - x = 9 - 3
বা, x = 6

অতএব বড় ছেলের বয়স = (2 × 6) = 12 বছর

১২৮.

The ratio of the present ages of P and Q is 3 : 4. Five years ago, the ratio of their ages was 5 : 7. Find their present ages.

ক
30, 40
খ
25, 30
গ
30, 35
ঘ
35, 40

সঠিক উত্তর: ক

30, 40

উত্তর

সঠিক উত্তর: ক

30, 40

ক

ব্যাখ্যা

Question: The ratio of the present ages of P and Q is 3 : 4. Five years ago, the ratio of their ages was 5 : 7. Find their present ages.

Solution:
As the ratio of their present ages is 3 : 4 ,
let their present ages be 3X and 4X.
So, 5 years ago, as the ratio of their ages was 5 : 7,
we can write,
(3x - 5) : (4x - 5) = 5 : 7
⇒ (3x - 5)/(4x - 5) = 5/7
⇒ 21x - 35 = 20x - 25
⇒ x = 10

Hence, their present ages are 3X = 30 and 4X = 40

১২৯.

The ages of Nishi and Rimi are in the ratio 6 : 5 respectively. After 9 years, the ratio of their ages will be 9 : 8. What is the difference in their ages now ?

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

সঠিক উত্তর: ক

3 years

উত্তর

সঠিক উত্তর: ক

3 years

ক

ব্যাখ্যা

Question: The ages of Nishi and Rimi are in the ratio 6 : 5 respectively. After 9 years, the ratio of their ages will be 9 : 8. What is the difference in their ages now?

Solution:
Let,
Nishi’s age be 6x years.
Then, Rimi’s age = 5x years.

Now
∴ (6x + 9)/(5x + 9) = 9/8
⇒ 8(6x + 9) = 9(5x + 9)
⇒ 48x - 45x = 81 - 72
⇒ 3x = 9
⇒ x = 3

∴ Difference in their ages = (6x - 5x) years
= x years
= 3 years.

১৩০.

The present ages of Rahim and Sakib 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?

ক
10 years
খ
8 years
গ
6 years
ঘ
12 years

সঠিক উত্তর: গ

6 years

উত্তর

সঠিক উত্তর: গ

6 years

গ

ব্যাখ্যা

Question: The present ages of Rahim and Sakib 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,
Rahim's age = 4x + 6
Sakib'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

Rahim's present age = 4 × 6 = 24 years
Sakib's present age = 5 × 6 = 30 years

∴ Difference = 30 - 24 = 6 years

১৩১.

The present ages of A and B are in the ratio 3 : 5. After 10 years, the ratio of their ages will be 4 : 6. What is the difference in their present ages?

ক
13 years
খ
15 years
গ
16 years
ঘ
20 years

সঠিক উত্তর: ঘ

20 years

উত্তর

সঠিক উত্তর: ঘ

20 years

ঘ

ব্যাখ্যা

Question: The present ages of A and B are in the ratio 3 : 5. After 10 years, the ratio of their ages will be 4 : 6. What is the difference in their present ages?

Solution:
Let the present ages be,
A = 3x and B = 5x

Ages after 10 years,
A = 3x + 10
B = 5x + 10

According to the problem, the ratio becomes 4 : 6
(3x + 10) : (5x + 10) = 4 : 6
⇒ (3x + 10)/(5x + 10) = 4/6
⇒ 3(3x + 10) =2(5x + 10)
⇒ 9x + 30 = 10x + 20
⇒ 10x - 9x = 30 - 20
∴ x = 10

A = 3 × 10 = 30 years
B = 5 × 10 = 50 years

∴ Difference = 50 - 30 = 20 years

১৩২.

The present age of Amir and his mother are in the ratio 2 : 5 respectively. Four years hence, the ratio of their ages become 5 : 11 respectively. What was Amir's present age in years?

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

সঠিক উত্তর: খ

16 years

উত্তর

সঠিক উত্তর: খ

16 years

খ

ব্যাখ্যা

Question: The present age of Amir and his mother are in the ratio 2 : 5 respectively. Four years hence, the ratio of their ages become 5 : 11 respectively. What was Amir's present age in years?

Solution:
Let
the present ages of Amir and his mother be 2x and 5x respectively.

ATQ,
(2x + 4) : (5x + 4) = 5 : 11
(2x + 4)/(5x + 4) = 5/11
⇒ 22x + 44 = 25x + 20
⇒ 25x - 22x = 44 - 20
⇒ 3x = 24
∴ x = 8

Amir's present age = (2 × 8) = 16 years

১৩৩.

Son's age is now one-third of father's age. In twelve years from now son's age will be one half of the father's age. What is the son's age in years now?

ক
ক) 6
খ
খ) 10
গ
গ) 12
ঘ
ঘ) 24

সঠিক উত্তর: গ

গ) 12

উত্তর

সঠিক উত্তর: গ

গ) 12

গ

ব্যাখ্যা

Question: Son's age is now one-third of father's age. In twelve years from now son's age will be one half of the father's age. What is the son's age in years now?

Solution:
ধরি, পিতার বয়স x বছর
পুত্রের বয়স x/৩ বছর

১২ বছর পর, পিতার বয়স = x + ১২ বছর
১২ বছর পর, পুত্রের বয়স = (x/৩) + ১২বছর
= (x + ৩৬)/৩ বছর

প্রশ্নমতে,
(x + ৩৬)/৩ = (x + ১২)/২
⇒ ২ (x + ৩৬) = ৩ (x + ১২)
⇒ ২x + ৭২ = ৩x + ৩৬
∴ x = ৭২ - ৩৬
= ৩৬

∴ পুত্রের বর্তমান বয়স = ৩৬/৩ বছর
= ১২ বছর

১৩৪.

The average age of A and B is 6 years more than the average age of B and C. C is how many years younger than A?

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

সঠিক উত্তর: গ

গ) 12 years

উত্তর

সঠিক উত্তর: গ

গ) 12 years

গ

ব্যাখ্যা

The average age of A and B = (A + B)/2
The average age of B and C = (B + C)/2
(A + B)/2 - (B + C)/2 = 6
A - C = 12
A = C + 12
C is 12 years younger than A.
---------------------------------------------
A ও B এর গড় বয়স B ও C এর গড় বয়সের চেয়ে ৬ বছর বেশি হলে, C, A এর চেয়ে কত বছরের ছোট?

A ও B এর গড় বয়স = (A + B)/2
B ও C এর গড় বয়স = (C + B)/2
সুতরাং
(A + B)/2 - (B + C)/2 = 6
A - C = 12
A = C + 12
C, A এর চেয়ে ১২ বছরের ছোট।

১৩৫.

Arif is 2 years older than Belal who is twice as old as Chandni. If the total of the ages of Arif, Belal and Chandni be 27, then how old is Belal?

ক
10 years
খ
11 years
গ
12 years
ঘ
13 years
ঙ
15 years

সঠিক উত্তর: ক

10 years

উত্তর

সঠিক উত্তর: ক

10 years

ক

ব্যাখ্যা

Question: Arif is 2 years older than Belal who is twice as old as Chandni. If the total of the ages of Arif, Belal and Chandni be 27, then how old is Belal?

Solution:

Let the present age of Chandni be x

So, Belal’s present age = 2x

And Arif’s present age = 2 + 2x

According to the question,

x + 2x + 2 + 2x = 27

⇒ 5x + 2 = 27

⇒ 5x = 25

⇒ x = 5

So, Belal’s age = 2 × 5 = 10 years

১৩৬.

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

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

সঠিক উত্তর: ঘ

14 years

উত্তর

সঠিক উত্তর: ঘ

14 years

ঘ

ব্যাখ্যা

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

Solution:

Let the son's age 10 years ago be x years

Then, man's age 10 years ago = 7x years

Son's present age = (x + 10) years,

Man's present age = (7x + 10) years

According to the question,
2[(7x + 10) + 2] = 5[(x + 10) + 2]

⇒ 2(7x + 12) = 5(x + 12)

⇒ 14x + 24 = 5x + 60

⇒ 9x = 36

⇒ x = 4

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

= (4 + 10) years

= 14 years

১৩৭.

Today is Sabit's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Sabit today?

ক
ক) 20 years
খ
খ) 25 years
গ
গ) 22 years
ঘ
ঘ) 27 year

সঠিক উত্তর: খ

খ) 25 years

উত্তর

সঠিক উত্তর: খ

খ) 25 years

খ

ব্যাখ্যা

Question: Today is Sabit's birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Sabit today?

Solution:
আজকে সাবিতের বয়স = x বছর
১ বছর পর সাবিতের বয়স হবে = (x + 1) বছর

শর্তমতে,
x + 1 = 2(x - 12)
⇒ x + 1 = 2x - 24
⇒ x = 25

১৩৮.

A man's present age is two-fifth of the age of his mother. After 9 years, he will be one-half of the age of his mother. How old is the mother at present?

ক
ক) 40 years
খ
খ) 43 years
গ
গ) 45 years
ঘ
ঘ) 48 years

সঠিক উত্তর: গ

গ) 45 years

উত্তর

সঠিক উত্তর: গ

গ) 45 years

গ

ব্যাখ্যা

Question: A man's present age is two-fifth of the age of his mother. After 9 years, he will be one-half of the age of his mother. How old is the mother at present?

Solution:
Let mother's age be x years
Then, man's age = 2x/5 years

ATQ,
(2x/5) + 9 = (x + 9)/2
⇒ (x/2) - (2x/5) = 9 - (9/2)
⇒ (5x - 4x)/10 = (18 - 9)/2
⇒ x/10 = 9/2
⇒ x = (9 × 10)/2
⇒ x = 9 × 5
∴ x = 45

∴ Mother's present age is 45 years

১৩৯.

Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?

ক
1 year
খ
2 years
গ
25 years
ঘ
Data inadequate
ঙ
None of these

সঠিক উত্তর: ঘ

Data inadequate

উত্তর

সঠিক উত্তর: ঘ

Data inadequate

ঘ

ব্যাখ্যা

Question: Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q's age?

Solution:

The difference of age between R and Q = The difference of age between Q and T.

Sum of age of R and T is 50
∴ (R + T) = 50.

R - Q = ?

ATQ,

R - Q = Q - T

∴ R + T = 2Q

Now given that, (R + T) = 50

50 = 2Q
∴ Q = 25.

Question is (R - Q) = ?

Here we know the value(age) of Q (25), but we don't know the age of R.

∴ (R - Q) cannot be determined.

১৪০.

The ratio of the present ages of Pranto and Qureshi is 4 : 5. Five years ago, the ratio of their ages was 7 : 9. Find their present ages? (In years)

ক
40, 50
খ
18, 25
গ
40, 60
ঘ
20, 25
ঙ
None of these

সঠিক উত্তর: ক

40, 50

উত্তর

সঠিক উত্তর: ক

40, 50

ক

ব্যাখ্যা

Question: The ratio of the present ages of Pranto and Qureshi is 4 : 5. Five years ago, the ratio of their ages was 7 : 9. Find their present ages? (In years)

Solution:

Their present ages be 4x and 5x.

5 years ago, the ratio of their ages was 7 : 9, then
(4x - 5) : (5x - 5) = 7 : 9

⇒ 36x - 45 = 35x - 35
⇒ x = 45 - 35
∴ x = 10.

Their present ages are: 40, 50.

১৪১.

Roni 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 Roni and Piyal's age?

ক
11 years
খ
15 years
গ
25 years
ঘ
30 years

সঠিক উত্তর: খ

15 years

উত্তর

সঠিক উত্তর: খ

15 years

খ

ব্যাখ্যা

Question: Roni 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 Roni 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 Roni is x

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

১৪২.

The ratio of the present age of father to that of son is 7:2. After 10 years their ages will be in the ratio of 9:4. The present ages of the father is -

ক
ক) 35 years
খ
খ) 40 years
গ
গ) 30 years
ঘ
ঘ) 25 years

সঠিক উত্তর: ক

ক) 35 years

উত্তর

সঠিক উত্তর: ক

ক) 35 years

ক

ব্যাখ্যা

ধরি
পিতার বর্তমান বয়স = ৭x বছর
পুত্রের বর্তমান বয়স = ২x বছর
প্রশ্নমতে,
(৭x + ১০)/(২x + ১০) = ৯/৪
২৮x + ৪০ = ১৮x + ৯০
২৮x - ১৮x = ৯০ - ৪০
১০x = ৫০
x = ৫

পিতার বর্তমান বয়স = (৭ × ৫)বছর = ৩৫ বছর

১৪৩.

The ratio of the ages of a father and his son is 8 : 3 respectively. Six years ago, the ratio of their ages was 3 : 1 respectively. What was the father's present age?

ক
56 years
খ
96 years
গ
78 years
ঘ
66 years

সঠিক উত্তর: খ

96 years

উত্তর

সঠিক উত্তর: খ

96 years

খ

ব্যাখ্যা

Question: The ratio of the ages of a father and his son is 8 : 3 respectively. Six years ago, the ratio of their ages was 3 : 1 respectively. What was the father's present age?

Solution:
ধরি, পিতার বর্তমান বয়স = 8x বছর
এবং পুত্রের বর্তমান বয়স = 3x বছর

ছয় বছর আগে,
পিতার বয়স = 8x − 6 বছর
পুত্রের বয়স = 3x − 6 বছর

প্রদত্ত শর্ত,
(8x − 6)/(3x − 6) = 3/1
9x - 18 = 8x - 6
9x - 8x = 18 - 6
x = 12

∴ পিতার বর্তমান বয়স = 8x = 8 × 12 = 96 বছর

১৪৪.

A mother is twice as old as her son. If 20 years ago, the age of the mother was 10 times the age of the son, what is the present age of the mother?

ক
38 years
খ
40 years
গ
43 years
ঘ
45 years

সঠিক উত্তর: ঘ

45 years

উত্তর

সঠিক উত্তর: ঘ

45 years

ঘ

ব্যাখ্যা

Question: A mother is twice as old as her son. If 20 years ago, the age of the mother was 10 times the age of the son, what is the present age of the mother?

Solution:
Let the age of son = x years
∴ Age of mother would be = 2x years

As per question 20 years ago;
10 (x - 20) = 2x - 20
⇒ 10x - 200 = 2x - 20
⇒ 10x - 2x = - 20 + 200
⇒ 8x = 180
⇒ x = 180/8
∴ x = 22.5

∴ Mother's age is = 2 × 22.5 = 45 years

১৪৫.

The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have a one year child.The average age of the family now is -

ক
ক) 19 years
খ
খ) 23 years
গ
গ) 28.5 years
ঘ
ঘ) 29.3 years

সঠিক উত্তর: ক

ক) 19 years

উত্তর

সঠিক উত্তর: ক

ক) 19 years

ক

ব্যাখ্যা

Sum of the present age of husband, wife and child
= (23 × 2 + 5 × 2) + 1 = 57 years
∴ Required average = (57/3) years
= 19 years

১৪৬.

One year ago Ikbal was 4 times as old as Atif. In 6 years, Ikbal's age exceeds the twice of Atif's age by 9 years. What is the current ratio of their age?

ক
11 : 3
খ
9 : 2
গ
12 : 5
ঘ
14 : 5

সঠিক উত্তর: ক

11 : 3

উত্তর

সঠিক উত্তর: ক

11 : 3

ক

ব্যাখ্যা

প্রশ্ন: One year ago Ikbal was 4 times as old as Atif. In 6 years, Ikbal's age exceeds the twice of Atif's age by 9 years. What is the current ratio of their age?

সমাধান:
ধরি,
1 বছর আগে আতিফের বয়স ছিল = x বছর
1 বছর আগে ইকবালের বয়স ছিল = 4x বছর

বর্তমানে আতিফের বয়স = x + 1 বছর
বর্তমানে ইকবালের বয়স = 4x + 1 বছর

6 বছর পর আতিফের বয়স = x + 1 + 6 = x + 7 বছর

6 বছর পর ইকবালের বয়স = 4x + 1 + 6 = 4x + 7 বছর

প্রশ্নমতে,
4x + 7 = 2(x + 7) + 9
⇒ 4x + 7 = 2x + 14 + 9
⇒ 2x = 16
∴ x = 8

অতএব, বর্তমানে তাদের বয়সের অনুপাত = (4 ⋅ 8 + 1) : (8 + 1)
= 33 : 9
= 11 : 3

১৪৭.

Rina is 15 years older than Tania. In 5 years, Rina will be twice as old as Tania will be at that time. How old is Tania now?

ক
18
খ
15
গ
12
ঘ
10

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: Rina is 15 years older than Tania. In 5 years, Rina will be twice as old as Tania will be at that time. How old is Tania now?

Solution:
Let,
The age of Tania = x
The age of Rina = x + 20

ATQ,
x + 20 = 2(x + 5)
⇒ x + 20 = 2x + 10
⇒ x = 10

১৪৮.

Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age?

ক
14 years and 28 years
খ
14 years and 30 years
গ
16 years and 32 years
ঘ
12 years and 28 years

সঠিক উত্তর: খ

14 years and 30 years

উত্তর

সঠিক উত্তর: খ

14 years and 30 years

খ

ব্যাখ্যা

Question: Ages of two persons differ by 16 years. If 6 year ago, the elder one be 3 times as old the younger one, find their present age?

Solution:
Let the age of an younger person be A
age of elder person = (A + 16)

According to the question, we have
3(A - 6) = (A + 16 - 6)
⇒ 3A - 18 = A + 10
⇒ 2A = 28
⇒ A = 14

∴ The younger and elder person age is 14 years old and 30 years old.

১৪৯.

The present ages of Arif, Sumon, and Saddam are in proportions 4 : 7 : 9. Before eight years, the sum of their ages was 56. What are their present ages in years?

ক
16, 28, 36
খ
16, 28, 40
গ
16, 30, 40
ঘ
Insufficient data

সঠিক উত্তর: ক

16, 28, 36

উত্তর

সঠিক উত্তর: ক

16, 28, 36

ক

ব্যাখ্যা

Question: The present ages of Arif, Sumon, and Saddam are in proportions 4 : 7 : 9. Before eight years, the sum of their ages was 56. What are their present ages in years?

Solution:
Then the Present age of Arif, Sumon, and Saddam would be 4x, 7x, 9x
Age before eight years:
4x - 8, 7x - 8, 9x - 8

According to question
4x - 8 + 7x - 8 + 9x - 8 = 56
⇒ 20x = 80
⇒ x = 80/20
∴ x = 4

Then their present is 4 × 4 = 16; 7 × 4 = 28 and 9 × 4 = 36 respectively.

১৫০.

A is two years older than B who is twice as old as C. If the average of the ages of A, B and C be 9, the how old is B?

ক
ক) 8 years
খ
খ) 10 years
গ
গ) 12 years
ঘ
ঘ) 18 years

সঠিক উত্তর: খ

খ) 10 years

উত্তর

সঠিক উত্তর: খ

খ) 10 years

খ

ব্যাখ্যা

Question: A is two years older than B who is twice as old as C. If the average of the ages of A, B and C be 9, the how old is B?

Solution:
তিনজনের বয়সের গড় ৯ বছর
বয়সের সমষ্টি = (৯ × ৩) বছর
= ২৭ বছর

ধরি, C এর বয়স x বছর
B এর বয়স 2x বছর
A এর বয়স 2x + 2

x + 2x + 2x + 2 = 27
⇒ 5x + 2 = 27
⇒ 5x = 25
∴ x = 5

B এর বয়স = 2x
= (2 × 5) বছর
= 10 বছর

১৫১.

If Riya's age is four times the age of Siya and if Riya's age is 24 years, find the age difference between Riya and Siya?

ক
ক) 2 years
খ
খ) 12 years
গ
গ) 18 years
ঘ
ঘ) 6 years

সঠিক উত্তর: গ

গ) 18 years

উত্তর

সঠিক উত্তর: গ

গ) 18 years

গ

ব্যাখ্যা

Let Siya's age = x
Then Riya's age = 4x
But given Riya's age = 24
=> 4x = 24
=> x = 6
Hence Siya's age = 6 years
=> The age difference = 24 - 6 = 18 years.

১৫২.

A man said to his son, "I was one-third of your present age when you were born". If the present age of the man is 72 years, find the present age of the son.

ক
48 years
খ
54 years
গ
56.7 years
ঘ
52 years

সঠিক উত্তর: খ

54 years

উত্তর

সঠিক উত্তর: খ

54 years

খ

ব্যাখ্যা

Question: A man said to his son, "I was one-third of your present age when you were born". If the present age of the man is 72 years, find the present age of the son.

Solution:
Present age of the son be P,
∴ he was born P years ago.
The age of the man was: (72 - P).
His age when the son was born should be equal to 1/3 of P.

∴ (72 - P) = P/3
⇒ 216 - 3P = P
⇒ 4P = 216
⇒ P = 54

১৫৩.

Sahin is younger than Ratul by 7 years. If the ratio of their ages is 7:9, find the age of Sahin.

ক
ক) 24.0
খ
খ) 25.5
গ
গ) 26.5
ঘ
ঘ) 27.5
ঙ
ঙ) 24.5

সঠিক উত্তর: ঙ

ঙ) 24.5

উত্তর

সঠিক উত্তর: ঙ

ঙ) 24.5

ঙ

ব্যাখ্যা

If Ratul age is x,
then Sahin age is x - 7,
so, (x - 7)/x = 7/9
9x - 63 = 7x
2x = 63
x = 31.5
So, Sahin age is = 31.5 - 7
= 24.5

১৫৪.

A man is 24 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
ক) 14
খ
খ) 18
গ
গ) 20
ঘ
ঘ) 22

সঠিক উত্তর: ঘ

ঘ) 22

উত্তর

সঠিক উত্তর: ঘ

ঘ) 22

ঘ

ব্যাখ্যা

Let,
The son's present age is x years.
Then, the man's present age is = (x + 24)
∴ (x + 24) + 2 = 2(x+ 2)
⇒ x + 26 = 2x + 4
⇒ x = 22

১৫৫.

Ten years ago, a man was eight 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
10 years
খ
12 years
গ
14 years
ঘ
18 years

সঠিক উত্তর: খ

12 years

উত্তর

সঠিক উত্তর: খ

12 years

খ

ব্যাখ্যা

Question: Ten years ago, a man was eight 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 = 8a years

∴ Son's present age = (a + 10) years
And man's present age = (8a + 10) years

ATQ,
2{(8a + 10) + 2} = 4{(a + 10) + 2}
⇒ 2(8a + 12) = 4(a + 12)
⇒ 16a + 24 = 4a + 48
⇒ 16a - 4a = 48 - 24
⇒ 12a = 24
⇒ a = 2

So, son's present age = (a + 10) = (2 + 10) = 12 years.

১৫৬.

Jobin is one year older than three times Lina's age. If their ages currently add up to 33 years, then how old will Jobin be in 4 years?

ক
23
খ
25
গ
27
ঘ
29
ঙ
31

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: Jobin is one year older than three times Lina's age. If their ages currently add up to 33 years, then how old will Jobin be in 4 years?

Solution:
Let Jobin = J and Lina = L.
Jobin is one year older than three times Lina's age in years:
J = 3L + 1

Currently, their ages add up to 33:
J + L = 33
⇒ (3L + 1) + L = 33
⇒ 4L = 32
⇒ L = 8

Lina is 8 years old. Jobin, from first equation, is
3L + 1
= 3(8) + 1
= 25

Jobin is 25 years old now. In four years he will be 29.

১৫৭.

A is two years older than B who is twice as old as C. If the total age of A, B and C is 32, Then How old is B?

ক
ক) 25 years
খ
খ) 20 years
গ
গ) 15 years
ঘ
ঘ) 12 years

সঠিক উত্তর: ঘ

ঘ) 12 years

উত্তর

সঠিক উত্তর: ঘ

ঘ) 12 years

ঘ

ব্যাখ্যা

Question: A is two years older than B who is twice as old as C. If the total age of A, B and C is 32, Then How old is B?

Solution:
Let
C's age be x years.
B's age = 2x years.
A's age = (2x + 2) years.
Now
∴ (2x + 2) + 2x + x = 32
⇒ 5x + 2 = 32
⇒ 5x = 32 - 2
⇒ 5x = 30
⇒ x = 6.

B's age = 2x = 12 years

১৫৮.

The father's age is five times his son's age. Six years after, the age of the father will be three times his son's age. The present ages, in years, of the son-

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

সঠিক উত্তর: খ

খ) 6 years

উত্তর

সঠিক উত্তর: খ

খ) 6 years

খ

ব্যাখ্যা

Question: The father's age is five times his son's age. Six years after, the age of the father will be three times his son's age. The present ages, in years, of the son-

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

প্রশ্নমতে,
5x + 6 = 3(x + 6)
⇒ 5x + 6 = 3x + 18
⇒ 2x = 18 - 6
⇒ x = 6

পুত্রের বর্তমান বয়স = 6 বছর

১৫৯.

Twice the age of X is thrice the age of Y. 8 years back, the difference between the ages of X and Y was 16 years. What is the present age of X?

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

সঠিক উত্তর: ক

ক) 48 years

উত্তর

সঠিক উত্তর: ক

ক) 48 years

ক

ব্যাখ্যা

2 times the age of X = 3 times the age of Y
2X = 3Y
⇒ X : Y = 3 : 2

Let present age of X and Y be 3a and 2a respectively
3a - 8 - (2a - 8) = 16
⇒ 3a - 2a = 16
⇒ a = 16

∴ The present age of X is 16 × 3 years = 48 years

১৬০.

Gulzar is four times as old as Hashem. 10 years ago, Gulzar was 9 times as old as Hashem. What will be the sum of their ages after 6 years?

ক
92
খ
88
গ
84
ঘ
82
ঙ
None

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: Gulzar is four times as old as Hashem. 10 years ago, Gulzar was 9 times as old as Hashem. What will be the sum of their ages after 6 years?

Solution:
Let,
The present age of Hashem is x years
∴ The present age of Gulzar is 4x years

ATQ,
4x - 10 = 9(x - 10)
⇒ 4x - 10 = 9x - 90
⇒ 5x = 80
∴ x = 16

Hashem's age after 6 years = x + 6 = 16 + 6 = 22 years
Gulzar's age after 6 years = 4x + 6 = 4 × 16 + 6 = 64 + 6 = 70 years

∴ The sum of their ages after 6 years = 70 + 22 = 92 years

১৬১.

The ratio of the present ages of P and Q is 3 : 4. Five years ago, the ratio of their ages was 5 : 7. Determine how old Q is right now.

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

সঠিক উত্তর: গ

40 years

উত্তর

সঠিক উত্তর: গ

40 years

গ

ব্যাখ্যা

Question: The ratio of the present ages of P and Q is 3 : 4. Five years ago, the ratio of their ages was 5 : 7. Determine how old Q is right now.

Solution:
As the ratio of their present ages is 3 : 4 ,

let,
their present ages be 3X and 4X.
So, 5 years ago, as the ratio of their ages was = 5 : 7,

we can write,
(3x - 5) : (4x - 5) = 5 : 7
⇒ (3x - 5)/(4x - 5) = 5/7
⇒ 21x - 35 = 20x - 25
⇒ x = 10

∴ their present age of Q = 4X = 40

১৬২.

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
8 years
খ
12 years
গ
10 years
ঘ
16 years

সঠিক উত্তর: ঘ

16 years

উত্তর

সঠিক উত্তর: ঘ

16 years

ঘ

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
⇒21x - 20x = 32 - 24
∴ x = 8

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

∴ Difference = 56 - 40 = 16 years

১৬৩.

Sachin is younger than Rohan by four years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

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

সঠিক উত্তর: ঘ

14 years

উত্তর

সঠিক উত্তর: ঘ

14 years

ঘ

ব্যাখ্যা

Question: Sachin is younger than Rohan by four years. If their ages are in the respective ratio of 7 : 9, how old is Sachin?

Solution:
Given that,
Sachin is 4 years younger than Rohan
Their ages are in the ratio 7 : 9

Let their ages are,
Sachin = 7x
Rohan = 9x

ATQ,
9x - 7x = 4
⇒ 2x = 4
∴ x = 2

Sachin age is = 7x = 7 × 2 = 14 years

১৬৪.

At present father and son have a combined age of 83. 10 years ago they had an age ratio of 7 : 2. What is the present age of the son?

ক
18 years
খ
24 years
গ
22 years
ঘ
26 years

সঠিক উত্তর: খ

24 years

উত্তর

সঠিক উত্তর: খ

24 years

খ

ব্যাখ্যা

Question: At present father and son have a combined age of 83. 10 years ago they had an age ratio of 7 : 2. What is the present age of the son?

Solution:
Let,
10 years ago their age were 7p and 2p

ATQ,
7p + 2p + 20 = 83
9p = 63
p = 7

present age of son is = 14 + 10 = 24 years

১৬৫.

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 are 27, then how old is B?

ক
ক) 7 years
খ
খ) 8 years
গ
গ) 9 years
ঘ
ঘ) 10 years

সঠিক উত্তর: ঘ

ঘ) 10 years

উত্তর

সঠিক উত্তর: ঘ

ঘ) 10 years

ঘ

ব্যাখ্যা

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 = 27
5x = 25
⇒ x = 5
Hence, B's age = 2x = 10 years.

১৬৬.

A man is 24 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
12 years
খ
14 years
গ
18 years
ঘ
20 years
ঙ
22 years

সঠিক উত্তর: ঙ

22 years

উত্তর

সঠিক উত্তর: ঙ

22 years

ঙ

ব্যাখ্যা

Let the son's present age be x years.
Then,
man's present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.

১৬৭.

Alfi got married 8 years ago. Today his age is 7/5 times his age at the time of marriage. Her daughter's age is 1/7 times her age. Her daughter's age is:

ক
2 years
খ
3 years
গ
4 years
ঘ
5 years
ঙ
None of these

সঠিক উত্তর: গ

4 years

উত্তর

সঠিক উত্তর: গ

4 years

গ

ব্যাখ্যা

Question: Alfi got married 8 years ago. Today his age is 7/5 times his age at the time of marriage. Her daughter's age is 1/7 times her age. Her daughter's age is:

Solution:
Let the age of Anita at the time of marriage be x
Now, hos age = x + 8

ATQ,
x + 8 = 7x/5
⇒ 5(x + 8) = 7x
⇒ 5x + 40 = 7x
⇒ 7x - 5x = 40
⇒ 2x = 40
∴ x = 20
Alfi's current age = 20 + 8 = 28 years
Her daughter's age = (1/7) × 28 = 4 years

১৬৮.

Ten years ago, the ratio of ages of S and T was 4 : 3. Now the ratio is 5 : 4. Find the present age of T.

ক
40
খ
50
গ
32
ঘ
36

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: Ten years ago, the ratio of ages of S and T was 4 : 3. Now the ratio is 5 : 4. Find the present age of T.

Solution:
Let the ages of S and T ten years ago be 4x and 3x.
Present ages of
S = 4x + 10 and T = 3x + 10

Now ratio = 5 : 4
⇒ (4x + 10)/(3x + 10) = 5/4
⇒ 4(4x + 10) = 5(3x + 10)
⇒ 16x + 40 = 15x + 50
⇒ 16x - 15x = 50 - 40
⇒ x = 10

∴ Present age of T = 3x + 10
= (10 × 3) + 10
= 30 + 10
= 40

১৬৯.

Sadia is currently three times older than Rina. Ten years ago, Sadia’s age was seven times Rina’s age.What will be the sum of their ages after 8 years?

ক
76
খ
56
গ
55
ঘ
80

সঠিক উত্তর: ক

উত্তর

সঠিক উত্তর: ক

ক

ব্যাখ্যা

Question: Sadia is currently three times older than Rina. Ten years ago, Sadia’s age was seven times Rina’s age.
What will be the sum of their ages after 8 years?

Solution:
Let Rina’s current age = x years
Sadia’s current age = 3x years

10 years ago:
Sadia’s age = 3x - 10
Rina’s age = x - 10

According to the question,
3x - 10 = 7(x - 10)
⇒ 3x - 10 = 7x - 70
⇒ - 4x = - 60
⇒ x = 15

So, Rina’s age = 15 years, Sadia’s age = 45 years

After 8 years:
Rina = 15 + 8 = 23
Sadia = 45 + 8 = 53

Sum = 23 + 53 = 76

১৭০.

The present age of a mother is the thrice that of her daughter. After 12 years, the age of the mother will be twice that of her daughter. The present age of the daughter is-

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

সঠিক উত্তর: খ

খ) 12 years

উত্তর

সঠিক উত্তর: খ

খ) 12 years

খ

ব্যাখ্যা

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

According to the question
3x + 12 = 2 (x + 12)
⇒ 3x + 12 = 2x + 24
⇒ x = 12
Present age of daughter = 12 years

১৭১.

Sabina got married 8 years ago. Today her age is 9/7 times her age at the time of her marriage. At present her daughter‘s age is one-sixth of her age. What was her daughter’s age 3 years ago?

ক
4 years
খ
3 years
গ
6 years
ঘ
Cannot be determined

সঠিক উত্তর: খ

3 years

উত্তর

সঠিক উত্তর: খ

3 years

খ

ব্যাখ্যা

Question: Sabina got married 8 years ago. Today, her age is 9/7 times her age at the time of her marriage. At present, her daughter's age is one-sixth of her age. What was her daughter's age 3 years ago?

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

according to the question,
x + 8 = (9/7) . x
⇒ 7x + 56 = 9x
⇒ 2x = 56
⇒ x = 28

∴ Sabina’s age now = (x + 8) years
= (28 + 8) = 36 years.

Her daughter’s age now = (1/6) × 36 years
= 6 years.
Her daughter’s age 3 years ago = (6 – 3) = 3 years.

১৭২.

Product of present age of Rahim and Latif is 2223 years and their present age ratio is 19 : 13 find the difference age of Rahim and Latif.

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

সঠিক উত্তর: ক

18 years

উত্তর

সঠিক উত্তর: ক

18 years

ক

ব্যাখ্যা

Question: Product of present age of Rahim and Latif is 2223 years and their present age ratio is 19 : 13 find the difference age of Rahim and Latif.

Solution:
Let, age of Rahim be 19x and age of Latif be 13x
Then, product of their ages = 19x × 13x = 247x²

Now,
247x² = 2223
⇒ x² = 9
∴ x = 3

Hence, required difference = 19x - 13x = 6x = 6 × 3 = 18 years

১৭৩.

The present age of the daughter is half of the present age of her mother. Ten years ago, her mother's age was thrice the age of her daughter. What is the present age of the daughter?

ক
35 years
খ
30 years
গ
25 years
ঘ
20 years

সঠিক উত্তর: ঘ

20 years

উত্তর

সঠিক উত্তর: ঘ

20 years

ঘ

ব্যাখ্যা

Question: The present age of the daughter is half of the present age of her mother. Ten years ago, her mother's age was thrice the age of her daughter. What is the present age of the daughter?

Solution:

Let the mother's age be 2x years
Then, the daughter's age = x years

According to the question,

2x - 10 = 3(x - 10)

⇒ 2x - 10 = 3x - 30

⇒ x = 20

∴ The present age of the daughter is 20 years.

১৭৪.

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

ক
17 years
খ
23 years
গ
18 years
ঘ
13 years

সঠিক উত্তর: ঘ

13 years

উত্তর

সঠিক উত্তর: ঘ

13 years

ঘ

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 ‘x’ years.

According to the question,
x + 15 = 5 (x - 5)
⇒ x + 15 = 5 x - 25
⇒ 4x = 40
⇒ x = 10
⇒ A’s present age = 10 years

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

১৭৫.

B is twice the age of C, and A is 2 years older than B. With their ages adding up to 42, what is A's age?

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

সঠিক উত্তর: খ

18 years

উত্তর

সঠিক উত্তর: খ

18 years

খ

ব্যাখ্যা

Question: B is twice the age of C, and A is 2 years older than B. With their ages adding up to 42, what is A's age?

Solution:
Let,
C is = x years old
B is 2x years old
A is (2x + 2) years old

Now,
2x + 2x + 2 + x = 42
⇒ 5x + 2 = 42
⇒ 5x = 40
∴ x = 8
A is (2 × 8) + 2 years old
= 16 + 2 years old
= 18 years old

১৭৬.

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 son?

ক
ক) 25 years
খ
খ) 20 years
গ
গ) 30 years
ঘ
ঘ) 40 years

সঠিক উত্তর: খ

খ) 20 years

উত্তর

সঠিক উত্তর: খ

খ) 20 years

খ

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 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

১৭৭.

The average of the ages of a man and his daughter is 34 years. If the respective ratio of their ages after four years from now is 14 : 5. what is daughter's present age?

ক
ক) 20 years
খ
খ) 52 years
গ
গ) 16 years
ঘ
ঘ) 34 years

সঠিক উত্তর: গ

গ) 16 years

উত্তর

সঠিক উত্তর: গ

গ) 16 years

গ

ব্যাখ্যা

Average age of man and his daughter = 34 years
Their total age = (34 × 2) years = 68 years
Let man's age be x years,
Then daughter age = (68 - x) years
∴(x + 4)/(68 - x + 4) =14/5
⇒5(x + 4) = 14(72 −x)
⇒5x + 20= 1008 − 14x
⇒19x =988
⇒ x =52

∴ Daughter's present age
= (68 - 52) years
= 16 years

১৭৮.

10 years ago, the average age of a family of 4 members was 24 years. Since then, two children have been born. Still, the average age of the family is the same today. If the two children differ in age by 2 years, find the present age of the younger child.

ক
2 years
খ
3 years
গ
4 years
ঘ
5 years

সঠিক উত্তর: খ

3 years

উত্তর

সঠিক উত্তর: খ

3 years

খ

ব্যাখ্যা

Question: 10 years ago, the average age of a family of 4 members was 24 years. Since then, two children have been born. Still, the average age of the family is the same today. If the two children differ in age by 2 years, find the present age of the younger child.

Solution:
Total age of 4 members, 10 years ago = (24 × 4) years = 96 years.
Total age of 4 members now = 4 × (24 + 10) = 136 years
Total age of 4 members now = (24 × 6) years = 144 years.

The sum of the ages of 2 children = (144 - 136) years
= 8 years

Let, the age of the younger child be x years
Then, age of elder child = (x + 2) years
So, x + x + 2 = 8
⇒ 2x = 6
∴ x = 3

So, the age of the younger child 3 years.

১৭৯.

After replacing an old member with a new member it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member?

ক
ক) 15
খ
খ) 20
গ
গ) 25
ঘ
ঘ) None of these

সঠিক উত্তর: ক

ক) 15

উত্তর

সঠিক উত্তর: ক

ক) 15

ক

ব্যাখ্যা

Question: After replacing an old member with a new member it was found that the average age of five members of a club is the same as it was 3 years ago. What is the difference between the ages of the replaced and the new member?

Solution:
(পাঁচ সদস্যের একটি গ্রুপে পুরাতন একজন সদস্যের পরিবর্তে নতুন একজন সদস্য নেওয়া হলে তাদের গড় বয়স ৩ বছর আগে যত ছিল তত হয়। পরিবর্তিত সদস্য এবং নতুন সদস্যের বয়সের পার্থক্য কত?)

এখানে
⇒ ৫ জন সদস্যের মোট বয়স ৩ বছর আগে যতই থাকুক ৩ বছর পর (৫ × ৩ ) = ১৫ বেড়ে যাওয়ার কথা।
⇒ কিন্তু নতুন সদস্য আসার কারণে ১৫ বছর কমে গিয়েছে, অর্থাৎ ৩ বছর আগের গড় বয়সের সমান হয়ে যায়।
⇒ অর্থাৎ নতুন সদস্যের বয়স পরিবর্তিত সদস্যের বয়স থেকে ১৫ বছর বেশি।

১৮০.

The present age of three persons are in the ratio of 4 : 7 : 9. Eight years ago, their total age was 56 years. In five years what will be the age of the oldest person?

ক
31 years
খ
21 years
গ
39 years
ঘ
41 years

সঠিক উত্তর: ঘ

41 years

উত্তর

সঠিক উত্তর: ঘ

41 years

ঘ

ব্যাখ্যা

Question: The present age of three persons are in the ratio of 4 : 7 : 9. Eight years ago, their total age was 56 years. In five years what will be the age of the oldest person?

Solution:
Present age ratio of three persons is 4 : 7 : 9

Let,
Their age is 4X, 7X and 9X respectively.

ATQ,
4X - 8 + 7X - 8 + 9X - 8 = 56
Or, 20X - 24 = 56
Or, 20X = 80
Or, X = 4

∴ The present age of the oldest person is = 9X = 9 x 4 = 36 years.
In five years, his age will be = (36 + 5 ) = 41 years.

১৮১.

7 years ago, the ages of A and B were in the ratio 4 : 5 and 7 years hence, they will be in the ratio 5 : 6. The present age of B is?

ক
73 years
খ
69 years
গ
81 years
ঘ
77 years

সঠিক উত্তর: ঘ

77 years

উত্তর

সঠিক উত্তর: ঘ

77 years

ঘ

ব্যাখ্যা

Question: 7 years ago, the ages of A and B were in the ratio 4 : 5 and 7 years hence, they will be in the ratio 5 : 6. The present age of B is?

Solution:
Let 7 years ago, ages of A and B were 4k years and 5k years, respectively.
Then, the present age of A = 4k + 7
and present age of B = 5k + 7

ATQ,
∴ (4k + 7 + 7)/(5k + 7 + 7) = 5/6
⇒ 24k + 84 = 25k + 70
⇒ k = 14
Hence, B's present age = 5 × 14 + 7 = 77 years

১৮২.

Five years ago the average of A, B, C, D was 45 years. By including X the present average of all the five is 49 years . Then the present age of X is-

ক
ক) 40 years
খ
খ) 45 years
গ
গ) 42 years
ঘ
ঘ) 49 years

সঠিক উত্তর: খ

খ) 45 years

উত্তর

সঠিক উত্তর: খ

খ) 45 years

খ

ব্যাখ্যা

Five years ago, the average age of A,B,C and D was 45 years

Sum of present age of A, B, C and D = 45 × 4 + 5 × 4 = 200 years
Present average age of A, B, C, D and X is 49
⇒ Sum of present age of A, B, C, D and X is (49 × 5) = 245 years
Present age of X is (245 - 200) = 45 years

∴ The present age of X is 45 years.

১৮৩.

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

ক
19
খ
29
গ
39
ঘ
49

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

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

Solution:
Let Bashir's present age = x years.
Then, A's present age = (x + 9) years.

ATQ,
(x + 9) + 10 = 2(x - 10)
⇒ x + 19 = 2x - 20
⇒ x = 39.

১৮৪.

A person's present age is two-fifth of the age of his father. After 10 years, he will be one half of the age of his father. What is the present age of the father?

ক
45 years
খ
50 years
গ
54 years
ঘ
48 years

সঠিক উত্তর: খ

50 years

উত্তর

সঠিক উত্তর: খ

50 years

খ

ব্যাখ্যা

Question: A person's present age is two-fifth of the age of his father. After 10 years, he will be one half of the age of his father. What is the present age of the father?

Solution:
Let the age of the person's father be 'x' years
∴ Age of the person = (2x/5)

After 10 years, age of the person's father = 'x + 10' years
Age of the person after 10 years = (2x/5) + 10 years

According to question,
(2x/5) + 10 = (1/2)(x + 10)
⇒ (2x/5) + 10 = (x/2) + 5
⇒ (x/2) - (2x/5) = 10 - 5
⇒ (5x - 4x)/10 = 5
⇒ x/10 = 5
⇒ x = 50

So, the present age of his father is 50 years

১৮৫.

If 10 years is subtracted from the present age of Zayed Khan and the reminder divided by 14, then you would get the present age of his grandson Sakib. If Sakib is 9 years younger than Bubli whose age is 14 years, then what is the present age of Zayed khan?

ক
ক) 60
খ
খ) 70
গ
গ) 74
ঘ
ঘ) 80

সঠিক উত্তর: ঘ

ঘ) 80

উত্তর

সঠিক উত্তর: ঘ

ঘ) 80

ঘ

ব্যাখ্যা

Bubli's age = 14 years
⇒ Sakib's age = (14 - 9) years
= 5 years
Let the present age of Zayed Khan be x years.
∴ (x - 10)/14 = 5
⇒ x - 10 = 70
⇒ x = 80 years.
Answer: Zayed Khan age is 80 years.

১৮৬.

Present ages of Sameer and Ananda are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Ananda's present age in years?

ক
22
খ
21
গ
20
ঘ
24

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

ব্যাখ্যা

Question: Present ages of Sameer and Ananda are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Ananda's present age in years?

Solution:
Let the present ages of Sameer and Ananda be 5x years and 4x years respectively.

Then,

⇒ 9(5x + 3) = 11(4x + 3)
⇒ 45x + 27 = 44x + 33
⇒ 45x - 44x = 33 - 27
⇒ x = 6
Anand's present age = 4x = 24 years

১৮৭.

The sum of ages of 5 siblings born at 2 years intervals is 60 years. What is the age of the elder sibling?

ক
10 years.
খ
14 years.
গ
16 years.
ঘ
18 years.

সঠিক উত্তর: গ

16 years.

উত্তর

সঠিক উত্তর: গ

16 years.

গ

ব্যাখ্যা

Question: The sum of ages of 5 siblings born at 2 years intervals is 60 years. What is the age of the elder sibling?

Solution:
Let youngest age = x
Ages = x, x + 2, x + 4, x + 6, x + 8

ATQ,
⇒ x + x + 2 + x + 4 + x + 6 + x + 8 = 60
⇒ 5x + 20 = 60
⇒ 5x = 60 - 20
⇒ 5x = 40
⇒ x = 40/5
∴ x = 8

∴ elder sibling = 8 + 8 = 16 years.

১৮৮.

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 years
খ
34 years
গ
28 years
ঘ
32 years

সঠিক উত্তর: ঘ

32 years

উত্তর

সঠিক উত্তর: ঘ

32 years

ঘ

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

১৮৯.

6 years ago, the ratio of the ages of Kamal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?

ক
16 years
খ
18 years
গ
20 years
ঘ
Cannot be determined

সঠিক উত্তর: ক

16 years

উত্তর

সঠিক উত্তর: ক

16 years

ক

ব্যাখ্যা

Question: 6 years ago, the ratio of the ages of Kamal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar's age at present?

Solution:
Let the ages of Kamal and Sagar 6 years ago be 6x and 5x years
Then,
(6x + 6 + 4)/(5x + 6 + 4) = 11/10
⇒ (6x + 10)/(5x + 10) = 11/10
⇒ 10(6x + 10) = 11(5x + 10)
⇒ 60x + 100 = 55x + 110
⇒ 5x = 10
∴ x = 2

Sagar's present age
= (5x + 6) years
= (5 × 2 + 6) years
= 16 years

১৯০.

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
ক) 35
খ
খ) 40
গ
গ) 50
ঘ
ঘ) None

সঠিক উত্তর: খ

খ) 40

উত্তর

সঠিক উত্তর: খ

খ) 40

খ

ব্যাখ্যা

প্রশ্ন: 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 :

সমাধান:
৩ বছর পূর্বে স্বামী, স্ত্রী ও সন্তানের বয়সের গড় = 27 বছর
৩ বছর পূর্বে স্বামী, স্ত্রী ও সন্তানের বয়সের সমষ্টি = 27 × 3 বছর
= 81 বছর

স্বামী, স্ত্রী ও সন্তানের বর্তমান বয়সের সমষ্টি = 81 + (3 × 3) = 81 + 9 = 90 বছর

৫ বছর পূর্বে স্ত্রী ও সন্তানের বয়সের গড় = 20 বছর
৫ বছর পূর্বে স্ত্রী ও সন্তানের বয়সের সমষ্টি = 20 × 2 বছর = 40 বছর

স্ত্রী ও সন্তানের বর্তমান বয়সের সমষ্টি = 40 + (2 × 5) = 50 বছর

স্বামীর বর্তমান বয়স = (90 - 50)বছর = 40 বছর

১৯১.

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
30 years
খ
34 years
গ
38 years
ঘ
40 years

সঠিক উত্তর: ঘ

40 years

উত্তর

সঠিক উত্তর: ঘ

40 years

ঘ

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

১৯২.

A couple has a son and a daughter. The age of the father is five times that of the son and the age of the daughter is one-third of that of her mother. The wife is 8 years younger to her husband and the sister is 4 years older than her brother. The mother's age is?

ক
44 years
খ
50 years
গ
32 years
ঘ
42 years

সঠিক উত্তর: ঘ

42 years

উত্তর

সঠিক উত্তর: ঘ

42 years

ঘ

ব্যাখ্যা

Question: A couple has a son and a daughter. The age of the father is five times that of the son and the age of the daughter is one-third of that of her mother. The wife is 8 years younger to her husband and the sister is 4 years older than her brother. The mother's age is?

Solution:
ধরি,
ছেলের বয়স = x বছর
পিতার বয়স = 5x বছর

আবার, ধরি মায়ের বয়স = y বছর
মেয়ের বয়স = y/3 বছর

প্রশ্নমতে,
5x - y = 8 ........... (1)
এবং,
⇒ y/3 - x = 4
⇒ y/3 = x + 4
∴ y = 3x + 12 ...........(2)

(1) নং হতে পাই,
⇒ 5x - y = 8
∴ y = 5x - 8
এখন y এর মান (2) নং এ বসিয়ে পাই
⇒ 5x - 8 = 3x + 12
⇒ 5x - 3x = 12 + 8
⇒ 2x = 20
⇒ x = 20/2
∴ x = 10
∴ পিতার বয়স = 5x = 5 × 10 = 50 বছর
∴ মায়ের বয়স = 50 - 8 = 42 বছর

১৯৩.

The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of second youngest
one?

ক
4
খ
10
গ
7
ঘ
13

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of second youngest
one?

Solution:
মনে করি,
সবচেয়ে ছোট শিশুটির বয়স x বছর

যেহেতু প্রত্যেক শিশুর জন্মের ব্যবধান 3 বছর

তাই 5 জন শিশুর বয়স হবে:
প্রথম অর্থাৎ সবচেয়ে ছোট শিশুটির বয়স x বছর
দ্বিতীয় অর্থাৎ দ্বিতীয় ছোট শিশুটির বয়স (x + 3) বছর
তৃতীয় শিশুটির বয়স (x + 3 + 3) বা (x + 6) বছর
চতুর্থ শিশুটির বয়স (x + 6 + 3) বা (x + 9) বছর
পঞ্চম শিশুটির বয়স (x + 9 + 3) বা (x + 12) বছর

প্রশ্নমতে,
x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
⇒ 5x + 30 = 50
⇒ 5x = 50 - 30
⇒ 5x = 20
⇒ x = 20/5
∴ x = 4

∴ দ্বিতীয় কনিষ্ঠ অর্থাৎ দ্বিতীয় ছোট শিশুটির বয়স = (4 + 3) বছর
= 7 বছর

১৯৪.

Shamsul is younger than Kabir by 7 years, and the ratio of their ages is 7 : 9. What is the age of Shamsul?

ক
20 years
খ
27years
গ
24.5 years
ঘ
26.5 years
ঙ
None of the above

সঠিক উত্তর: গ

24.5 years

উত্তর

সঠিক উত্তর: গ

24.5 years

গ

ব্যাখ্যা

Question: Shamsul is younger than Kabir by 7 years, and the ratio of their ages is 7 : 9. What is the age of Shamsul?

Solution:
Let the ages of Shamsul and Kabir be 7x and 9x respectively.

According to the Question:
7x = 9x - 7
⇒ 2x = 7
∴ x = 7/2 = 3.5

So, Shamsul's age = 7x = 7 × 3.5 = 24.5 years

১৯৫.

The ratio of present age A and B is 13 : 10 after 2.5 years their ratio will be 32 : 25 then find the present age of A.

ক
45.5
খ
35
গ
40.5
ঘ
50.5

সঠিক উত্তর: ক

45.5

উত্তর

সঠিক উত্তর: ক

45.5

ক

ব্যাখ্যা

Question: The ratio of present age A and B is 13 : 10 after 2.5 years their ratio will be 32 : 25 then find the present age of A.

Solution:
Let, present age of A = 13x and present age of B = 10x

According to question:
(13x + 2.5)/(10x + 2.5) = 32/25
⇒ (13x + 2.5) × 25 = (10x + 2.5) × 32
⇒ 325x + 62.5 = 320x + 80
⇒ 5x = 17.5
⇒ x = 3.5

∴ Present oge of A = 13 × 3.5 = 45.5

১৯৬.

The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:

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

সঠিক উত্তর: খ

20 years

উত্তর

সঠিক উত্তর: খ

20 years

খ

ব্যাখ্যা

Question: The sum of the present ages of a father and his son is 60 years. Six years ago, father's age was five times the age of the son. After 6 years, son's age will be:

Solution:
Let the present ages of the son and father be x and (60 -x) years respectively.
Then, (60 - x) - 6 = 5(x - 6)
⇒ 54 - x = 5x - 30
⇒ 6x = 84
⇒ x = 14
∴ Son's age after 6 years = (x + 6) = 20 years.

১৯৭.

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
7
খ
8
গ
9
ঘ
10
ঙ
11

সঠিক উত্তর: ঘ

উত্তর

সঠিক উত্তর: ঘ

ঘ

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.

১৯৮.

Rahim’s present age is two-fifths of the age of his father. After 8 years, Rahim will be one-half of the age of his father. What is the present age of the father?

ক
20
খ
30
গ
40
ঘ
50

সঠিক উত্তর: গ

উত্তর

সঠিক উত্তর: গ

গ

ব্যাখ্যা

Question: Rahim’s present age is two-fifths of the age of his father. After 8 years, Rahim 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, Rahim's present age = p × (2/5) year

After 8 years father will be = (p + 8) year
After 8 years Rahim will be = {(2p/5) + 8} year

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

So, Present age of father = 40 year.

১৯৯.

5 years earlier X was triple the age of Y. At present the sum of their age is 70. What is the present age of X?

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

সঠিক উত্তর: গ

50 years

উত্তর

সঠিক উত্তর: গ

50 years

গ

ব্যাখ্যা

Question: 5 years earlier X was triple the age of Y. At present the sum of their age is 70. What is the present age of X?

Solution:
Let,
5 years ago Y was a years old
X was = 3a years old.

ATQ,
a + 3a + 5 + 5 = 70
or, 4a = 70 - 10
∴ a = 15

∴ the present age of X is = (3 × 15) + 5
= 50 years

২০০.

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

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

সঠিক উত্তর: খ

2 times

উত্তর

সঠিক উত্তর: খ

2 times

খ

ব্যাখ্যা

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

Solution:
Let,
Rakib'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 Rakib's age.