Question

Two-thirds 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

The correct option is C $2205$

Let the number be $x$

Then, $\frac{1}{7}$ of $x$ is $\frac{1}{7}x$

And $\frac{2}{3}$ of $\frac{1}{7}x$ is $\frac{2}{21}x$

But this number is $87.5\%$ of $240$

$\frac{2}{21}x=\frac{87.5}{100}\times 240$

$\Rightarrow 20x=87.5\times 24\times 21$

$\Rightarrow 20x=44100$

$\Rightarrow x=2205$

Then, the number is $2205$.