Question

the present ages of Renu and Sonu are in ratio 8 ratio 9 after 5 years the ratio of the ages will be nine ratio 10 find their present ages​

Answer 1

☞ The present ages of Renu and Sonu are in ratio 8 : 9

Let present age of Renu be 8M and present age of Sonu be 9M.

• After 5 years.

Age of Renu = 8M + 5

And age of Sonu = 9M + 5

☞ And the ratio of their ages after 5 years will be 9 : 10.

• A.T.Q.

=> $\dfrac{8M\:+\:5}{9M\:+\:5}$ = $\dfrac{9}{10}$

Cross-multiply them

=> 10(8M + 5) = 9(9M + 5)

=> 80M + 50 = 81M + 45

=> 80M - 81M = 45 - 50

=> - M = - 5

=> M = 5

_______________________________

Present age of Renu = 8M = 8(5) = 40 years.

And

Present age of Sonu = 9M = 9(5) = 45 years.

_____________ [ANSWER]

» $\dfrac{8M\:+\:5}{9M\:+\:5}$ = $\dfrac{9}{10}$

• Put value of M in above eq

=> $\dfrac{8(5)\:+\:5}{9(5)\:+\:5}$ = $\dfrac{9}{10}$

=> $\dfrac{45}{50}$ = $\dfrac{9}{10}$

=> $\dfrac{9}{10}$ = $\dfrac{9}{10}$

___________ [HENCE VERIFIED]