Question

. The ages of Neha and Hema are in the ratio
9:7. Ten years ago, their ages were in the
ratio 7:5. Find their present ages. ​

Answer 1

Let there ages be x and y respectively.

Then, x/y=9/7

7x=9y

x=9y/7

ten years ago

x-10/y-10=7/5

5x-50=7y-70

5x-7y=-20

45y/7 -7y=-20

45y-49y=-140

-4y=-140

y=140/4

y=35

So age of Hema =35

Age of Neha=9×35/7=45

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Answer 2

$\large \bold{ \underline{ \underline{ \: Answer : \: \: \: }}}$

$\to$ The present age of Hema = 35

$\to$ The present age of Neha = 45

$\large \bold{ \underline{ \underline{ \: Explaination : \: \: \: }}}$

Let ,

The present age of Neha = x

The present age of Hema = y

According to the question ,

$\to \frac{x}{y} = \frac{9}{7} \\ \\ \to 7x = 9y</p><p> \\ \\ \to</p><p>x= \frac{9y}{7} \: \: - - - - \: eq (i)$

Ten years ago ,

$\to \frac{x - 10}{y - 10} = \frac{7}{5} \\ \\ \to</p><p>5x-50=7y-70</p><p> \\ \\ \to</p><p>5x-7y=-20</p><p> \\ \\ \to \frac{45y}{7 } - 7y= - 20 \\ \\ \to</p><p>45y-49y=-140 \\ \\ \to</p><p></p><p>-4y=-140</p><p> \\ \\ \to</p><p>y= \frac{140}{4} \\ \\ \to</p><p> </p><p>y=35$

Put the value of y = 35 in eq (i)

$\to x = \frac{9 \times 35}{7} \\ \\\to x = 45$

$\therefore$ The age of Hema and Neha is 35 and 45