Question

The ages of Arun and Rahul are in the ratio 7:5. Ten years hence the ratio of their ages will be in the ratio 19:15. Find their ages.

Answer 1

• Let present age of Arun be 7M and present age of Rahul be 5M.

» 10 years later

• Age of Arun = 7M + 10

• Age of Rahul = 5M + 10

» Also said that after 10 years.. ratio of their ages will be 19:15

A.T.Q.

=> $\dfrac{7M\:+\:10}{5M\:+\:10}$ = $\dfrac{19}{15}$

Cross-multiply them

=> 15(7M + 10) = 19(5M + 10)

=> 105M + 150 = 95M + 190

=> 105M - 95M = 190 - 150

=> 10M = 40

=> M = 4

_____________________________

Present age of Arun = 7M = 7(4) = 28 years

Present age of Rahul = 5M = 5(4) = 20 years.

____________ $\bold{[ANSWER]}$

_____________________________

✡ Put value of M in this equation $\dfrac{7M\:+\:10}{5M\:+\:10}$ = $\dfrac{19}{15}$

=> $\dfrac{7(4)\:+\:10}{5(4)\:+\:10}$ = $\dfrac{19}{15}$

=> $\dfrac{28\:+\:10}{20\:+\:10}$ = $\dfrac{19}{15}$

=> $\dfrac{38}{30}$ = $\dfrac{19}{15}$

=> $\dfrac{19}{15}$ = $\dfrac{19}{15}$

__________ [HENCE VERIFIED]

Answer 2

Let present age of Arun be 7M and present age of Rahul be 5M.

» 10 years later

• Age of Arun = 7M + 10

• Age of Rahul = 5M + 10

» Also said that after 10 years.. ratio of their ages will be 19:15

A.T.Q.

=>  =  

Cross-multiply them

=> 15(7M + 10) = 19(5M + 10)

=> 105M + 150 = 95M + 190

=> 105M - 95M = 190 - 150

=> 10M = 40

=> M = 4

_____________________________

Present age of Arun = 7M = 7(4) = 28 years

Present age of Rahul = 5M = 5(4) = 20 years.

____________  

_____________________________

✡ Put value of M in this equation  =  

=>  =  

=>  =  

=>  =  

=>  =  

__________ [HENCE VERIFIED]