Question

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Answer 1

Given :

Present Ages of A and B are in the ratio 7:5 .

After 10 years their ages will be in the ratio 9:7 .

To Find :

Present Ages of A and B .

Solution :

$\longmapsto\tt{Let\:Present\:age\:of\:A\:be=7x}$

$\longmapsto\tt{Let\:Present\:age\:of\:B\:be=5x}$

After 10 years :

$\longmapsto\tt{Age\:of\:A=7x+10}$

$\longmapsto\tt{Age\:of\:B=5x+10}$

A.T.Q :

$\longmapsto\tt{\dfrac{7x+10}{5x+10}=\dfrac{9}{7}}$

$\longmapsto\tt{7(7x+10)=9(5x+10)}$

$\longmapsto\tt{49x+70=45x+90}$

$\longmapsto\tt{49x-45x=90-70}$

$\longmapsto\tt{4x=20}$

$\longmapsto\tt{x=\cancel\dfrac{20}{4}}$

$\longmapsto\tt\bf{x=5}$

Value of x is 5 .

Therefore :

$\longmapsto\tt{Present\:Age\:of\:A=7(5)}$

$\longmapsto\tt\bf{35\:yrs}$

$\longmapsto\tt{Present\:Age\:of\:B=5(5)}$

$\longmapsto\tt\bf{25\:yrs}$