Out of a total 85 children playing badmin… | Answer

Subject

Quantitative Aptitude

Topic

Percentage

Out of a total 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 the total number of boys playing badminton is 60% of the total number of boys. The number of children playing only table tennis is 40% of the total number of children and a total of 12 children play badminton and table tennis both. What is the number of girls playing only badminton?
Reading

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Data inadequate

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None of these

Explanation

Let us consider the number of boys to be x. Number of girls = 70% of x Therefore, x + 70% of x = 85

\begin{array}{l} \Rightarrow {\rm{}}x + \frac{{70 \times x}}{{100}} = 85\\ \Rightarrow {\rm{}}x + \frac{{7x}}{{10}} = 85 \end{array}

⇒ 10x + 7x = 850 ⇒ 17x = 850 ⇒ x = 850/17 ⇒ x = 50 Therefore, number of boys = 50 and the number of girls are (85 – 50) = 35 Number of boys playing only badminton = 50% of boys

= \frac{{50}}{{100}} \times 50{\rm{}} = {\rm{}}25{\rm{}}

∴ Total number of boys playing Table Tennis = 50 – 25 = 25 Total number of boys playing badminton = 60% of boys =

\frac{{60}}{{100}} \times 50 = {\rm{}}30

∴ Total number of boys playing both table tennis and badminton = 30 – 25 = 5 ∴ Total number of boys playing only Table Tennis = 25 – 5 = 20 Number of children playing only table tennis = 40% of all children

= {\rm{}}\frac{{40}}{{100}} \times 85 = {\rm{}}34

∴ Number of girls playing only Table tennis = 34 – 20 = 14 Total number of children playing badminton and tennis both = 12 ∴ total number of girls playing both badminton and table tennis both = 12 – 5 = 7 Therefore, number of girls playing only badminton = 35 – (14 + 7) = 14

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Explanation

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