Question

The present ages of A and B in the ratio 7:5 . ten years later, their ages will be in the ratio 9:5 . Find their present ages.​

Answer 1

Answer:

35 and 25 years i think so

Answer 2

Correct Question :

• The present ages of A and B in the ratio 7:5 . ten years later, their ages will be in the ratio 9:7 . Find their present ages .

Given :

• The present ages of A and B are in ratio of 7:5

• Ten years later, there ages will be in the ratio of 9:7

To find :

• Their present ages

Solution :

Now , let us take unknown entity as x

» Present age of A = 7x years

» Present age of B = 5x years

10 years from now ,

» Age of A = (7x+10) years

» Age of B = (5x+10) years

$\:\:\:\: \star\:\large \underline {\sf{According\:to\:the\:question\::}}$

$\rightarrow \sf (7x\:+\:10)\::\:(5x\:+\:10)\:=\:(9)\::\:(7)$

$\rightarrow \sf \dfrac{(7x\:+\:10)}{(5x\:+\:10)}\:=\: \dfrac{(9)}{(7)}$

$\rightarrow \sf 7(7x\:+\:10)\:=\:9(5x\:+\:10)$

$\rightarrow \sf 49x\:+\:70\:=\:45x\:+\:90$

$\rightarrow \sf 49x\:-\:45x\:=\:90\:-\:70$

$\rightarrow \sf 4x\:=\:20$

$\rightarrow \sf x\:=\: \cancel \dfrac{20}{4}$

$\:\:\:\: \large {\underline{\boxed{\sf{Value\:of\:x\:=\:5}}}}$

• Their Present Ages :

• Present age of A = 7x = 7×5 = 35 years

• Present age of B = 5x = 5×5 = 25 years

★ Therefore, the present age of A is 35 years and present age of B is 25 years

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