Question

If $$15\mathrm{\%}$$ of 40 is greater than $$25\mathrm{\%}$$ of a number by 2, the number is
A. 14
B. 16
C. 18
D. 20

Answer 1

Hint: We can solve this question by converting a given statement in terms of algebraic equations. For this we let an unknown number equal to any variable and write the equation according to the given statement in terms of that variable.

Complete step by step solution:
Let the number is x.
 As given in the question,$$15\mathrm{\%}$$ of 40 is greater than $$25\mathrm{\%}$$ of x by 2.
Hence we can write the difference between $$15\mathrm{\%}$$ of 40 and $$25\mathrm{\%}$$ of x is 2.
$$\Rightarrow 15\mathrm{\%}of40-25\mathrm{\%}ofx=2$$
$$\Rightarrow {\displaystyle \frac{15}{100}}\times 40-{\displaystyle \frac{25}{100}}\times x=2$$
$$\Rightarrow {\displaystyle \frac{600}{100}}-{\displaystyle \frac{25x}{100}}=2$$
$$\Rightarrow {\displaystyle \frac{600-25x}{100}}=2$$
$$\Rightarrow 600-25x=200$$.
$$\Rightarrow 600-200=25x$$
$$\Rightarrow 25x=400$$
$$\Rightarrow x={\displaystyle \frac{400}{25}}$$
$$\Rightarrow x=16$$

Hence the required number is 16. So option B is correct.

Note: In general percentage means out of 100. If we have to find x% of a , we simply multiply x and a then divide by 100. We can write it as
$\Rightarrow x\mathrm{\%}ofa={\displaystyle \frac{x}{100}}\times a$