Discussion
In an examination, a student was asked to find \(\frac{3}{14}\) of a certain number. By mistake, he found \(\frac{3}{4}\) of it. His answer was 150 more than the correct answer. The given number is
Answer: B
The number is 280.
Let the number be \(N\). The mistaken answer exceeds the correct one by 150:
\[ \begin{aligned} \tfrac{3}{4}N - \tfrac{3}{14}N &= 150 \\ \tfrac{21 - 6}{28}N &= 150 \\ \tfrac{15}{28}N &= 150 \\ N &= 280 \end{aligned} \]
Check: \(\frac{3}{4}\) of 280 is 210 and \(\frac{3}{14}\) of 280 is 60, and \(210 - 60 = 150\). With 500, 180 or 160 the difference would not be 150; for example \(\frac{15}{28}\) of 500 is about 268.
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