Question

The ages of ravish and shikha are in the ratio 3:8.6 year hence, their age will be in the ratio 4:9 .the present age of ravish is​

Answer 1

according to the question, the ages of ravish and shikha are in the ratio 3 : 8 and after 6 years, their age will be in the ratio 4 : 9

let the present age of ravish and shikha be 3x and 8x respectively.

therefore after 6 years their ages will be (3x + 6) and (8x + 6)

➡ (3x + 6)/(8x + 6) = 4/9

cross multiplying..

➡ 9(3x + 6) = 4(8x + 6)

➡ 27x + 54 = 32x + 24

➡ 27x - 32x = 24 - 54

➡ -5x = -30

➡ x = -30/-5

➡ x = 6

hence, present age of :-

• ravish = 3x

= 3 × 6

= 18 yrs

• shikha = 8x

= 8 × 6

= 48 yrs

Answer 2

» The ages of ravish and shikha are in the ratio 3:8

• Let present age of Ravish be 3M and present age of Shikha be 8M.

» 6 years later ..

Age of Ravish = 3M + 6

Age of Shikha = 8M + 6

» Then the ratio will be 4:9

A.T.Q.

=> $\dfrac{3M\:+\:6}{8M\:+\:6}$ = $\dfrac{4}{9}$

Cross-multiply them

=> 9(3M + 6) = 4(8M + 6)

=> 27M + 54 = 32M + 24

=> 27M - 32M = 24 - 54

=> - 5M = - 30

=> 5M = 30

=> M = 30/5

=> M = 6

_______________________________

$\textbf{Present age of Ravish}$ = 3M = 3 × 6

$\textbf{= 18 years.}$

$\textbf{Present age of Shikha}$ = 8M = 8 × 6

$\textbf{= 48 years}$

___________ [ANSWER]

_______________________________

✡ $\dfrac{3M\:+\:6}{8M\:+\:6}$ = $\dfrac{4}{9}$

Put value of M in above equation

=> $\dfrac{3(6)\:+\:6}{8(6)\:+\:6}$ = $\dfrac{4}{9}$

=> $\dfrac{18\:+\:6}{48\:+\:6}$ = $\dfrac{4}{9}$

=> $\dfrac{24}{54}$ = $\dfrac{4}{9}$

=> $\dfrac{4}{9}$ = $\dfrac{4}{9}$

_______ [HENCE VERIFIED]

________________________________