Question

If 37.5% of a number is 450 then 87.5% of the number will be _______,
A. 825
B. 1,175
C. 1,050
D. 1,250

Answer 1

Hint: In this question it is given that 37.5% of a number is 450, then we have to find 87.5% of that number. So to find the solution we first need to find that number after that we can easily find 87.5% of that number.
So for this you have to know that if you have given ‘r% of a number x’, then we can write it as $$\dfrac{r}{100} \times x$$.

Complete step-by-step answer:
Here it is given that 37.5% of a number is 450.
So for this let us consider that the number be x.
Therefore, 37.5% of a number is 450 can be written as,
$$\dfrac{37.5}{100} \times x=450$$
$$\Rightarrow \dfrac{37.5\times 2}{100\times 2} \times x=450$$ [by multiplying numerator and denominator by 2]
$$\Rightarrow \dfrac{75}{200} \times x=450$$
$$\Rightarrow \dfrac{75x}{200} =450$$
$$\Rightarrow 75x=450\times 200$$
$$\Rightarrow 75x=90000$$
$$\Rightarrow x=\dfrac{90000}{75}$$
$$\Rightarrow x=\dfrac{75\times 1200}{75}$$
$$\Rightarrow x=1200$$
Therefore the number is 1200,
Now we have to find 87.5% of 1200,
Therefore,
87.5% of 1200
$$=\dfrac{87.5}{100} \times 1200$$
$$=\dfrac{87.5\times 1200}{100}$$
$$=87.5\times 12$$ [canceling 100 from numerator and denominator]
$$=1050$$
Therefore we can say that 87.5% of the number will be 1,050.
Hence the correct option is option C.

Note: While solving this type of question you need to know that, how r% of x is equals to $$\dfrac{rx}{100}$$, this is because, here % defines $$\dfrac{1}{100}$$ and ‘of’ implies $$\times$$, so from here we can write,
r% of x=$$r\times \dfrac{1}{100} \times x=\dfrac{rx}{100}$$