Question:

A number decreased by $27 \frac{1}{2} \%$ gives 87 . The number is

(a) 58

(b) 110

(c) 120

(d) 135

Solution:

(c) 120

Let the required number be $\mathrm{x}$. Then, we have:

$x-\left(27 \frac{1}{2} \%\right.$ of $\left.x\right)=87$

$\Rightarrow \mathrm{x}-\left(\frac{55}{2} \%\right.$ of $\left.\mathrm{x}\right)=87$

$\Rightarrow \mathrm{x}-\left(\mathrm{x} \times \frac{55}{2} \times \frac{1}{100}\right)=87$

$\Rightarrow \mathrm{x}-\frac{11 \mathrm{x}}{40}=87$

$\Rightarrow \frac{29 \mathrm{x}}{40}=87$

$\Rightarrow \mathrm{x}=\left(87 \times \frac{40}{29}\right)$

$\Rightarrow \mathrm{x}=120$