Question

14. Presentages of Anu and are on the rate 4:5. Eight years from now the ratio of the ages will be 5:6. Find their presentare age ​

Answer 1

CORRECT QUESTION :

Present ages of Anu and Raj are in the ratio 4:5 . Eight years from now the ratio of the ages will be 5:6. Find their present ages .

Given :

• Present ages of Anu and Raj are in the ratio 4:5 .
• Eight years from now the ratio of the ages will be 5:6.

To Find :

• Present Age of Anu and Raj .

Solution :

$\longmapsto\tt{Let\:Present\:age\:of\:Anu\:be=4x}$

$\longmapsto\tt{Let\:Present\:age\:of\:Raj\:be=5x}$

After 8 years :

$\longmapsto\tt{Age\:of\:Anu=4x+8}$

$\longmapsto\tt{Age\:of\:Raj=5x+8}$

A.T.Q :

$\longmapsto\tt{\dfrac{4x+8}{5x+8}=\dfrac{5}{6}}$

$\longmapsto\tt{6(4x+8)=5(5x+8)}$

$\longmapsto\tt{24x+48=25x+40}$

$\longmapsto\tt{24x-25x=40-48}$

$\longmapsto\tt{-1x=-8}$

$\longmapsto\tt\bf{x=8}$

Value of x is 8 .

Therefore :

$\longmapsto\tt{Present\:age\:of\:Anu=4(8)}$

$\longmapsto\tt\bf{32\:yrs}$

$\longmapsto\tt{Present\:age\:of\:Raj=5(8)}$

$\longmapsto\tt\bf{40\:yrs}$

Answer 2

Given :-

Present ages of Anu and Raj are on the ratio 4:5. Eight years from now the ratio of the ages will be 5:6.

To Find :-

Present ages

Solution :-

Let the ratio be 4x and 5x

After 8 years

4x + 8/5x + 8 = 5/6

5(5x + 8) = 6(4x + 8)

25x + 40 = 24x + 48

25x - 24x = 48 - 40

x = 8

Therefore

Age of Anu = 4x = 4(8) = 32 years

Age of Raj = 5x = 5(8) = 40 years