Question

Age of A and B 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 present age of A be 8M and present age of B be 11M

After 10 years..

• Age of A = 8M + 10

• Age of B = 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

=> 15M = 30

=> M = 2

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Present age of A = 8M = 8(2) = 16 years

Present age of B = 11M = 11(2) = 22 years

__________ [ ANSWER ]

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Answer 2

Age of A = 8x + 10

Age of B = 11x + 10

According to question;

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

Cross-multiply

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

128x + 160 = 143x + 130

15x = 30

x = 2

Ae of A = 16 years

Age of B = 22 years