Question

Mr A is 3 years elder to Mrs A. One-fifth of Mr
A's age is 3 years more that one-eighth of Mrs
age. How old are Mr and Mrs A?
​

Answer 1

Topic

Linear Equations

Given

Mr. A is 3 years elder to Mrs. A.

One - fifth of Mr.A's age is 3 years more that One - Eighth of Mrs. A's age.

To Find

How old are Mr. A and Mrs. A ?

Solution

Let age of Mrs. A be 'x'.

Age of Mr. A is 3 years more than the age of Mrs. A.

So, age of Mr. A will be '( x + 3 )'.

One-Fifth of Mr. A's age is 3 years more than one-eighth of Mrs. A's age.

$\frac{1}{5}( x + 3 ) = \frac{1}{8}x + 3$

$\frac{1}{5}x + \frac{3}{5} = \frac{1}{8}x + 3$

$\frac{1}{5}x - \frac{1}{8}x = 3 - \frac{3}{5}$

$\frac{8x - 5x}{40} = \frac{15 - 3}{5}$

$\frac{3x}{40} = \frac{12}{5}$

Now, cross multiply.

( 3x ) × 5 = 12 × 40

15x = 480

$x = \frac{480}{15}$

x = 32

So, the age of Mrs. A is 32 years and

the age of Mr. A is ( x + 3 )

32 + 3

35 years

Answer

Age of Mr. A is 35 years and the age of Mrs. A is 32 years.