Question

A student who secures $20\%$ marks in an examination fails by $30$ marks. Another student who secures $32\%$ gets $42$ marks more than those required to pass. The percentage of marks required to pass is:

• A. $20$
• B. $25$
• C. $28$
• D. $30$

Answer 1

Correct option is B. $25$

Let the total number of marks be $x$ units

Thus, $20\%$ of $x=\frac{20}{100}\times x=0.2x$

Also, $32\%$ of $x=\frac{32}{100}\times x=0.32x$ units

Therefore, according to the question,

$\Rightarrow 0.2x+30=0.32x-42$

$\Rightarrow 0.32x-0.2x=30+42$

$\Rightarrow 0.12x=72$

$\Rightarrow x=\frac{72}{0.12}=600$

Hence, Passing marks are $=\frac{20}{100}\times 600+30=150$

Thus, Percentage of marks required to pass $=\frac{150}{600}\times 100=25\%$