Out of a total of 85 children playing Badminton or Table Tennis or both, total number of girls in the group is 70\% of the total number of boys in the group, the number of boys playing only Badminton is 50\% of the number of boys and total number of boys playing Badminton is 60\% of the total number of boys. Number of children only playing table Tennis is 40\% of the total number of children and a total of 12 children play both Badminton and Table Tennis. What is the number of girls playing only Badminton? [DMRC-Customer Relations Assistant (CRA) Exam, 2016]
(a)16
(b)14
(c)17
(d)None of these
Answer
Answer (as printed): B
Explanation
Boys: Girls - 10 : 7 $$\begin{aligned} & \therefore \text { Boys }=\frac{10}{17} \times 85=50 \\ & \text { Girls }=(85-50)=35 \end{aligned}$$ Boys who play only badminton $50 \%$ of $50=\frac{50 \times 50}{100}=25$ Boys who play badminton $$=\frac{60 \times 50}{100}=30$$ Children who play only table $$\text { Tennis }=\frac{85 \times 40}{100}=34$$ Children who play badminton and table tennis = 12 Boys who play only table tennis $=50-30=20$ ∴ Girls who play only table tennis $=34-20=14$ Girls who play badminton and table tennis $$=12-(30-25)=12-30+25=37-30=7$$ ∴ Girls who play only badminton $$=35-14-7=35-21=14$$
Explanation as extracted from the printed page; notation may be imperfect.