Question

The ages of a and b are in the ratio 7:8 six years ago their ages were in the ratio 5:6 find their present ages??

Answer 1

Given :-

• The ages of a and b are in the ratio 7:8 six years ago their ages were in the ratio 5:6.

To Find :-

• Present Age's of A and B

Answer :-

• Present Age of A = 7x = 7(3) = 21 years
• Present Age of B = 8x = 8(3) = 24 years

Explaination :-

Let Present age of A be 7x and present age of B be 8x

★ 6 years ago,

• Age of A = 7x - 6
• Age of B = 8x - 6

⌾ According to Question :-

→ 7x - 6/8x - 6 = 5/6

By cross multiplication we get :

→ (7x - 6)6 = 5(8x - 6)

→ 42x - 36 = 40x - 30

→ 42x - 40x = -30 + 36

→ 2x = 6

→ x = 6 ÷ 2

→ x = 3

Hence,

• Present Age of A = 7x = 7(3) = 21 years
• Present Age of B = 8x = 8(3) = 24 years

Answer 2

Given :

The ages of A and B are in the ratio = 7:8 .

Six years ago their ages were in the ratio = 5:6.

To Find :

Present ages .

Solution :

Present age of A and B = 7x , 8x

Six years ago their ages were in the ratio 5:6 .

• Age of A was = 7x - 6
• Age of B was = 8x - 6

Now :

$\sf{\dfrac{7x-6}{8x-6}=\dfrac{5}{6}}$

6(7x - 6) = 5(8x - 6)

42x - 36 = 40x - 30

42x - 40x = -30 + 36

2x = 6

x = 6/2

x = 3

So , The value of x is 3 .

Hence :

Present Age of A = 7x

= 7(3)

= 21

Present age of B = 8x

= 8(3)

= 24

Therefore , Present ages of A and B are 21 years and 24 years .