Question

In Times Model School, 60% of the students are boys. In an aptitude test, 80% of the girls scored more than 40 marks (out of a maximum possible 150 marks). If 60% of the total students scored more than 40 marks in the same test, find the fraction of the boys who scored 40 marks or less?
(a) 3/5
(b) 6/7
(c) 5/7
(d) 7/15
(e) none of these

Answer 1

(e) non of these






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Answer 2

The fraction of the boys who scored 40 marks or less is $\frac{8}{15}$. Here, answer is option(e) none of these.

Step-by-step explanation:

Let the total number of students = 100

60% of the students are boys.

Number of boys = 60% x 100 = $\frac{60}{100} \times 100$ = 60

Number of girls = 100 - 60 = 40

80% of the girls scored more than 40 marks.

Number of girls scored more than 40 marks = $\frac{80}{100}\times 40$ = 32

60% of the total students scored more than 40 marks.

Total number of students scored more than 40 marks = $\frac{60}{100}\times 100$ = 60

Number of boys scored more than 40 marks = 60 - 32 = 28

Number of boys scored 40 marks or less = 60 - 28 = 32

Fraction of boys who scored 40 marks or less = $\frac{32}{60} = \frac{8}{15}$

Hence, the fraction of the boys who scored 40 marks or less is $\frac{8}{15}$. Here, answer is option(e) none of these.