The difference between increased number by increasing 8% of given number and decreased number by decreasing 7% of the same number is 75. What is the number ?

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Solution

Let the required nuber be $x$
$∴ 8 %$ of $x = \frac{8 x}{100}$
Therefore, Increased number $= x + \frac{8 x}{100} = \frac{108 x}{100}$
Similarly, the number decreased by $7$
Now, $\frac{108 x}{100} - \frac{93 x}{100} = \frac{15 x}{100}$ But, actual difference $= 75$
So, $\frac{15 x}{100} = 75$
Thus, $x = \frac{75 \times 100}{15} = 5 \times 100 = 500$
Hence, the required number is $500$

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