Question

A boy was asked to multiply a number by 7/8. Instead he divided the number by 7/8 and got the result 15/14 more than what he should have got if he had multiplied the number by 7/8. The number is -

Answer 1

Let the number be x

According to the question

$\frac{x}{7/8} -x\frac{7}{8} =\frac{15}{14}$

$\frac{8x}{7} -\frac{7x}{8}=\frac{15}{4}$

$\frac{64x-49x}{56} =\frac{15}{4}$

$\frac{15x}{56}=\frac{15}{4}$

$x=\frac{56}{4} =14$

Answer 2

Answer-

The number is 4 .

Solution-

Let us assume the number was x and the product he could have gotten was y, so

$\Rightarrow x\times \frac{7}{8}=y\\ \Rightarrow x=y\times \frac{8}{7}$

Instead, he divided the number x with 7/8, and got 15/14 more than y,

$\Rightarrow \frac{x}{\frac{7}{8}}=y+\frac{15}{14} \\\\ \Rightarrow \frac{8x}{7}=y+\frac{15}{14}$

Putting the values of x in second equation,

$\Rightarrow \frac{8(y\times \frac{8}{7})}{7}=y+\frac{15}{14}$

$\Rightarrow \frac{64y}{49}=y+\frac{15}{14}$

$\Rightarrow \frac{64y}{49}-y=\frac{15}{14}$

$\Rightarrow y(\frac{64}{49}-1)=\frac{15}{14}$

$\Rightarrow \frac{15}{49}y=\frac{15}{14}$

$\Rightarrow y=\frac{28}{7}=4$

Therefore, the number is 4.