Question

75% of a number is equal to 15. Find the number.
[a] 20
[b] 30
[c] 16
[d] 12

Answer 1

Hint: Assume that the number is equal to x. Express the given statement in the form of a mathematical equation in terms of x. Solve for x to get the value.

Complete step-by-step answer:
Let x be the number, 75% of whose is 15.
Hence we have 75%$\text{ of }x=15$.
Meaning of percentage:
Cent means 100 in English. Hence percent means out of 100. Hence 75% means 75 out of 100.
Hence 75%$\text{ of }x$ means $\dfrac{75}{100}\times x$
Writing $\dfrac{75}{100}$ in lowest terms:
We will first find gcd(75,100) using the long division method (Euclid’s Division Algorithm).
$\begin{align}
  & 100=75+25 \\
 & 75=25\times 3+0 \\
\end{align}$
Hence gcd(75,100) = 25
Dividing numerator and denominator by 25, we get
$\dfrac{75}{100}=\dfrac{\dfrac{75}{25}}{\dfrac{100}{25}}=\dfrac{3}{4}$
Hence 75%$\text{ of }x=\dfrac{3x}{4}$
Hence, we have $\dfrac{3x}{4}=15$
Multiplying both sides by 4, we get
3x = 60
Dividing both sides by 3, we get
x =20
Hence the number whose 75% is 15 is x.
Hence option [a] is correct.

Note: Alternatively, we can use the unitary method to solve the question.
We have,
75 percent of the number = 15
1 percent of the number $=\dfrac{15}{75}$
100 percent of the number $=\dfrac{15}{75}\times 100=\dfrac{1500}{75}=20$
Hence option [a] is correct.