Question

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five years ago the ratio of the age of a and b is 4:7. the ratio of their ages 2 years from now will be 9:14 .
what will be the answer?
1) 66
2)55
3)65
4)69​

Answer 1

Given :-

Five years ago the ratio of the age of a and b is 4:7. the ratio of their ages 2 years from now will be 9:14

To Find :-

Sum of their ages

Solution :-

Let

Age of a = x

Age of b = y

5 years ago

$\sf \dfrac{x-5}{y-5}=\dfrac{4}{7}$

$\sf 7(x-5)=4(y-5)$

$\sf 7x-35=4y-20$

$\sf 7x-4y=-20+35$

$\sf 7x-4y=15(1)$

2 years from now

$\sf \dfrac{x+2}{y+2}=\dfrac{9}{14}$

$\sf 14(x+2)=9(y+2)$

$\sf 14x+28=9y+18$

$\sf 14x-9y=18-28$

$\sf 14x-9y=-10(2)$

On multiplying Eq. 1 by 2

$\sf 2(7x-4y)=2(15)$

$\sf 14x-8y=30(3)$

On subtracting 2 and 3

$\sf 14x-9y-(14x-8y)=-10-30$

$\sf 14x-9y-14x+8y=-40$

$\sf -y=-40$

$\sf y=40$

From 1

$\sf 7x-4y=15$

$\sf 7x-4(40)=15$

$\sf 7x-160=15$

$\sf 7x=15+160$

$\sf 7x=175$

$\sf x=\dfrac{175}{7}$

$\sf x=25$

Sum of their ages

$\sf x+y$

$\sf 25+40$

$\sf 65(Option \;C)$