Question

One year ago, the ratio of gaurav's and sachin's age was 6: 7 respectively. Four years hence, this ratio would become 7: 8. How old is sachin ?

Answer 1

let Gaurav present age be x years and Sachin age be y years
$\frac{x - 1}{y - 1} = \frac{6}{7} \\ 7(x - 1) = 6(y - 1) \\ 7x - 7 = 6y - 6 \\ 7x - 6y = 1.....1$
according to 2nd condition
$\frac{x + 4}{y + 4} = \frac{7}{8} \\ 8x + 32 = 7y + 28 \\ 8x - 7y = 28 - 32 \\ 8x - 7y = - 4....2$
multiply 1 with -7
we get
$- 49x + 42y = - 7....3$
multiply 2 with 6
we get
$48x - 42y = - 24....4$
adding 3 and 4 we get
$- x = - 31 \\ x = 31$
put x=31 in 1
$7 \times 31 - 6y = 1 \\ - 6y = 1 - 217 \\ - 6y = - 216 \\ y = 36$
the present age of Sachin is 36 years.
hope this helps you:-))))
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Answer 2

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