Find Father's Age and Son's Age

---

Q1. Father's Age and Son's Age

Q. A father's age is 6 times his son's age. After 4 years, the father's age will be 4 times the son's age. Find their present ages.

Solution:

Let the son's present age = x years

Father's present age: $$=6x$$

After 4 years: Son's age: $$x+\mathrm{4,}$$Father's age: 6x + 4

According to the question:

6x + 4 = 4(x + 4)

6x + 4 = 4x + 16

6x − 4x = 16 − 4

2x = 12

 x = 6

Therefore,

Son's present age = 6 years

Father's present age: 6 × 6 = 36

Ans: Son = 6 years. Father = 36 years

Short Trick: Age Problem

Father : Son = 6 : 1

After 4 years:

Father : Son = 4 : 1

Difference in ratio: $$6-4=2$$

The 2 parts = 4 years

$$1\text{ part}=2\text{ years}$$

So, Son's present age: 1× 6 = 6 years​

Father's present age: 6 × 6 = 36 years​

Ans: Son = 6 years, Father = 36 years

Trick: Age ratio difference → divide the added years

======================================

Q. The present ages of A and B are in the ratio 4 : 5. After 6 years, their ages will be in the ratio 5 : 6. What is B's present age ?

(A) 24 years  (B) 30 years  (C) 36 years  (D) 40 years

Solution:

Let the present ages of A and B be 4x and 5x.

After 6 years:

4x + 6 / 5x + 6 = 5/6

Cross-multiply:

6(4x+6) = 5(5x+6)

24x + 36 = 25x + 30

x = 6

Therefore,

B′s present age = 5x = 5×6 = 30 years

Ans: (B) 30 years

​=============================

Q. The present ages of A and B are in the ratio 3 : 4. After 5 years, their ages will be in the ratio 4 : 5. What is B's present age ?

(A) 15 years  (B) 20 years  (C) 25 years  (D) 30 years

Solution:

Let present ages be 3x and 4x.

After 5 years: 3x +5 / 4x + 5 = 4/5

Cross-multiply: 5(3x + 5) = 4(4x + 5) 

                       15x + 25 = 16x + 20

                                     x = 5

Therefore,

B = 4x = 4 × 5 = 20 years 

Ans: (B) 20 years

======================================

Q. The sum of the ages of a father and son is 60 years. The father is 4 times as old as his son. Find their ages.

Solution

1st: Assume son's age = x

Father's age = 4x

2nd: Form the equation

4x + x = 60 

5x = 60

x = 12

3rd: Find their ages

Son's age: x=12 years

Father's age: 4x = 4×12 = 48 years 

Ans: Father = 48 years, Son = 12 years

Trick

Ratio = Father : Son = 4 : 1

Total parts = 5

60 ÷ 5 = 12 

So: Son = 12 years, Father = 48 years.

==============================