A scored 30\% marks and failed by 15 marks. B scored 40\% marks and obtained 35 marks more than those required to pass. The pass percentage is
(a)33\%
(b)38\%
(c)43\%
(d)46\%
Answer
Answer (as printed): A
Explanation
Let total marks $=x$. Then, (30\% of $x)+15=(40 \%$ of $x)-35$ $$\Leftrightarrow \frac{30}{100} x+15=\frac{40}{100} x-35 \Leftrightarrow \frac{1}{10} x=50 \Leftrightarrow x=500 .$$ So, passing marks $=(30 \%$ of 500$)+15$ $$=\left(\frac{30}{100} \times 500+15\right)=165 .$$ ∴ Pass percentage $=\left(\frac{165}{500} \times 100\right) \%=33 \%$.
Explanation as extracted from the printed page; notation may be imperfect.