Question

age of Sachin and Jatin are in the ratio 8 : 11 .after 10 years the ratio of their age will be 13 :16 .what is the difference between their ages ?

Answer 1

• Let age of Sachin be 8M and age of Jatin be 11M.

» 10 years later..

• Age of Sachin = 8M + 10

• Age of Jatin = 11M + 10

» And ratio of their ages is 13:16

A.T.Q.

=> $\dfrac{8M\:+\:10}{11M\:+\:10}$ = $\dfrac{13}{16}$

Cross-multiply them

=> 16(8M + 10) = 13(11M + 10)

=> 128M + 160 = 143M + 130

=> 128M - 143M = 130 - 160

=> - 15M = - 30

=> M = 2

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Age of Sachin = 8M = 8 × 2 = 16 years

Age of Jatin = 11M = 11 × 2 = 22 years

________________ [ANSWER]

________________________________

✡ $\dfrac{8M\:+\:10}{11M\:+\:10}$ = $\dfrac{13}{16}$

Put value of M = 2 in above equation

=> $\dfrac{8(2)\:+\:10}{11(2)\:+\:10}$ = $\dfrac{13}{16}$

=> $\dfrac{16\:+\:10}{22\:+\:10}$ = $\dfrac{13}{16}$

=> $\dfrac{26}{32}$ = $\dfrac{13}{16}$

=> $\dfrac{13}{16}$ = $\dfrac{13}{16}$

___________ [HENCE VERIFIED]

Answer 2

Let age of Sachin = 8x

Age of Jatin = 11x

Age of Sachin after 10 yrs = 8x + 10

Age of Jatin after 10 yrs = 11x + 10

A.T.Q

8x + 10/11x + 10 = 13/16

16 (8x + 10) = 13 (11x + 10)

128x + 160 = 143x + 130

128x - 143x = 130 - 160

15x = 30

x = 2

Age of Sachin = 16 yrs

Jatin = 22 yrs