A candidate, appearing for an examination, was asked to find 3/14 of a certain number but mistakenly, he found 3/4 of it. When he cross checked his answer, he found his answer was 150 more than the correct answer. Which number was given in the examination for this calculation?
Solution
Correct Answer: Option B
Let the number be x.
The candidate was asked to find 3/14, i.e. 3/14 of x but mistakenly, he found ¾ of x and difference between these answers = 150
¾ of x – 3/14 of x = 150
\(\Rightarrow \frac{3}{4} \times x\;-\frac{3}{{14}} \times x = 150\)
\(\Rightarrow \frac{{3x}}{4}-\frac{{3x}}{{14}} = 150\)
\(\Rightarrow 3x \times \left( {\frac{1}{4}-\frac{1}{{14}}} \right) = \;150\)
⇒3x (5/28) =150
\(\Rightarrow x = \frac{{150 \times 28}}{{5 \times 3}} = 280\)
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