Question

Five years ago the ratio of the ages of a and b was 3:2 and after five years it will become 5:4 find their present age

Answer 1

Answer:

Given:

• Five years ago the ratio of the ages of a and b was 3:2

• after five years it will become 5:4 find their present age

To find:

• Their present ages.

Solving Question:

We are given the ratio of ages of 'a' and 'b' .So let 'x' be  the age of 'a' and 'y' be that of 'b'  their ages

( Five years ago )

Five years ago the ratio of the ages of a and b was 3:2

⇒ $\dfrac{x-5}{y-5}=\dfrac{3}{2}\\\\\implies 2(x-5)=3(y-5)\\\\\implies 2x-10=3y-15\\\\\implies 2x-3y=-5....equ(1)$

after five years it will become 5:4

$\dfrac{x+5}{y+5}=\dfrac{5}{4}\\\\\implies 4(x+5)=5(y+5)\\\\\implies 4x+20=5y+25\\\\\implies 4x-5y=5........equ(2)$

Solution:

multiply 2 in .equ(1);

2(2x -3y = -5)

⇒ 4x -6y = -10 ......equ(3)

Equate the equ(2) and equ(3)

4x -6y = -10

4x -5y = 5

..........................

we get, - y = -15

or, y = 15

Substitute it in equ(1)

2x -3y = -5

2x -3(15) = -5

or, 2x -45 = -5

or, 2x = 40

or, x = 20

∴ The age of 'a' is 20 and 'b' is 15 years respectively.