There are 96 boys and 84 girls in a class. If 60% of the total students leave the class and 'n' numb

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03 May 2022 Ratio & Proportion

There are 96 boys and 84 girls in a class. If 60% of the total students leave the class and 'n' number of girls joined again and the ratio of boys to girls become 4:5. Which of the following CAN NOT be the value of 'n' ?

OPtion

1) 45
2) 27
3) 81
4) 63
5) 72
6) 36
7) 42
8) 18
9) 54
10) None of these

Solution

Total number of students = 96+84 = 180
Number of students left = 60% of 180 = 108
Let in 108 students who left, there are x boys and (108-x) girls
After joining of n girls, new ratio of boys and girls = (96 - x) / [84 - (108-x) + n] = 4/5
4n = 576 - 9x
n = 144 - (9/4)x
Now, x (multiple of 4) can have the values from 24 to 60 to get +ve integer value of n and number of girls left (108-x) is less than 84.
For x=24, n=90
For x=28, n=81
.
.
For x=60, n=9
We observe that values of 'n' is multiple of 9 upto 90.
So, from the given options 42 can not be the value of 'n'

Correct Option: 7 Best Solution (2)

G.S.Kantharao   2 years AGO

Tal strength=96+84=180
Left over =60%=108
Remaining =72
Joined n
So total =72+n
Ratio =4:5

So (72+n) exactly divisible with 9
So n cannot be 42
My option is 7👈

Like? Yes (4) | No   

Dr.Dipin Singh   2 years AGO

Total students =180
When 60% sudents left abd n girls joined, remaining students are 72+n.
As new ratio us 4:5, total number of students now should be multiple of 9 abd hence n should be multiple of 9.
From given options, 42 is not multiple of 9.

Hence option 7

Like? Yes (2) | No (1)