Question

Two third of one seventh of a number is \[87.5\%\] of \[240\].What is the number?
A. 2670
B. 2450
C. 2205
D. 1470

Answer 1

Hint:A percentage is a dimensionless number or ratio expressed as a fraction of \[100\]. It is often denoted using the percent sign, “$\text{%}$”. Two-thirds is an amount that is two out of three equal parts of it. Similarly one-seventh is an amount that is one out of seven equal parts.

Complete step by step answer:
We need to find the unknown number. Let us consider the number be \[x\].
Given, \[\dfrac{2}{3}\ \]of \[\dfrac{1}{7}\ \] of a number say \[x\] is \[87.5\%\] of \[240\].
\[\Rightarrow \dfrac{2}{3} \times \dfrac{1}{7}\left(x\right) = \dfrac{87.5}{100} \times 240 \\ \]
\[\Rightarrow \dfrac{2}{21}x = \dfrac{87.5}{10} \times 24 \\ \]
By cross multiplying, we get,
\[20x = 87.5 \times 24 \times 21 \\ \]
\[\Rightarrow 20x = 44100.0 \\ \]
\[\Rightarrow x = \dfrac{44100}{20}\]
By dividing, we get
\[\therefore x = 2205\]
The number is \[2205\].

Therefore, the correct answer is option C.

Note:If we add, subtract, multiply or divide by the same number on both sides of a given algebraic equation, then both sides will remain equal. The percentage formula $\text{Percentage} = \dfrac{\text{Part}}{\text{Whole}} \times 100\% $ can be used to find any parameter in the equation given the other parameters. The abbreviations used to represent the percentage are “pct” or ”pc”.