Discussion
If \(\frac{2}{3}\)rd part of a number is greater by 7 than \(\frac{3}{5}\)th of it, then the number is
Answer: B
The number is 105.
Let the number be \(x\). Two thirds of it exceeds three fifths of it by 7:
\[ \begin{aligned} \frac{2x}{3} - \frac{3x}{5} &= 7 \\ \frac{10x - 9x}{15} &= 7 \\ x &= 105 \end{aligned} \]
Check: \(\frac{2}{3} \times 105 = 70\) and \(\frac{3}{5} \times 105 = 63\), which differ by 7. The other options give differences of 4, 10 and 8.
A quicker route: the difference of the two fractions is \(\frac{2}{3} - \frac{3}{5} = \frac{1}{15}\) of the number, and that equals 7, so the number is \(15 \times 7 = 105\).
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