Q57
ArithmeticPercentage, Profit & Loss
In an examination, 55% of the candidates failed in English, 65% failed in Mathematics, whereas 24% failed in both. Find the percentage of candidates passed in the both subjects.
- a.4%
- b.4.5%
- c.5%
- d.5.5%
Answer: (A) 4%
Candidates who failed in at least one subject = $55+65-24=96\%$ (inclusion–exclusion, since the 24% who failed in both would otherwise be counted twice). Therefore those who passed in both subjects = $100-96=4\%$. As a check: failed in English only = $55-24=31\%$, failed in Mathematics only = $65-24=41\%$, failed in both = 24%, and $31+41+24=96\%$. A Venn diagram of two overlapping circles makes such questions quick.