In an examination, 35\% candidates failed in one subject and 42\% failed in another subject while 15\% failed in both the subjects. If 2500 candidates appeared at the examination, how many passed in either subject but not in both?
(a)325
(b)1175
(c)2125
(d)None of these
Answer
Answer (as printed): B
Explanation
Failed in 1st subject $=\left(\frac{35}{100} \times 2500\right)=875$. $$\begin{aligned} & \text { Failed in 2nd subject }=\left(\frac{42}{100} \times 2500\right)=1050 \\ & \text { Failed in both }=\left(\frac{15}{100} \times 2500\right)=375 \end{aligned}$$ Failed in 1st subject only $=(875-375)=500$. Failed in 2nd subject only $=(1050-375)=675$. $$\begin{array}{r} \therefore \quad \text { Passed in 2nd only }+ \text { Passed in 1st only } \\ =(675+500)=1175 . \end{array}$$
Explanation as extracted from the printed page; notation may be imperfect.