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CAT 2017 Slot 1 — QA Question 9

PercentageEasy

The number of girls appearing for an admission test is twice the number of boys. If 30% of the girls and 45% of the boys get admission, the percentage of candidates who do not get admission is:

Answer & solution

Correct answer: 65

  • A

    35

  • B

    50

  • C

    60

  • 65

Solution

Easy

Take boys =b=b, then girls =2b=2b. Count admitted boys and girls, add them, and compare to the total of 3b3b candidates. "Do not get admission" is the complement.

1

Set the counts. Girls are twice the boys.

boys=b,girls=2b⇒ total=3b\begin{aligned} &\text{boys}=b,\quad \text{girls}=2b\\ &\Rightarrow\ \text{total}=3b \end{aligned}
2

Admitted candidates. 45%45\% of boys and 30%30\% of girls.

admitted=0.45b+0.30(2b)⇒ =0.45b+0.60b=1.05b\begin{aligned} &\text{admitted} = 0.45b + 0.30(2b)\\ &\Rightarrow\ = 0.45b + 0.60b = 1.05b \end{aligned}
3

Percentage not admitted. Admitted fraction first, then complement.

1.05b3b×100%=35%(admitted)⇒ 100%−35%=65%\begin{aligned} &\frac{1.05b}{3b}\times 100\% = 35\% \quad\text{(admitted)}\\ &\Rightarrow\ 100\% - 35\% = 65\% \end{aligned}
65%65\%

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CAT 2017 Slot 1 QA Q9: The number of girls appearing for an admission test is twice the number of boys. If 30% of the girls and 45% o — Solution | TheCATExam