Question

The mean annual college fees paid by all students in a college is 55 lakhs. The mean annual college fees paid
by male and female students of the college are 40 lakhs and 60 lakhs respectively. Then, the percentages of male
students studying in the college is
a)60%
b)50%
c)20%
d)25%
e)30%

Answer 1

20 hope it helps to the answer

Answer 2

The percentages of male students studying in the college is 25% [ The correct option is d) 25% ]

Given :

• The mean annual college fees paid by all students in a college is 55 lakhs

• The mean annual college fees paid by male and female students of the college are 40 lakhs and 60 lakhs respectively

To find :

The percentages of male students studying in the college is

a) 60%

b) 50%

c) 20%

d) 25%

e) 30%

Solution :

Step 1 of 2 :

Form the equation to calculate percentages of male students studying in the college

Let number of male students = m and number of female students = f

Since mean annual college fees paid by all students in a college is 55 lakhs

∴ Total college fees paid by all students

= 55(m + f) lakhs

The mean annual college fees paid by male and female students of the college are 40 lakhs and 60 lakhs respectively

∴ Total college fees paid by all students

= (40m + 60f) lakhs

By the given condition

$\displaystyle \sf 55(m + f) = 40m + 60f$

Step 2 of 2 :

Calculate percentages of male students studying in the college

$\displaystyle \sf 55(m + f) = 40m + 60f$

$\displaystyle \sf{ \implies } 55m +55 f = 40m + 60f$

$\displaystyle \sf{ \implies } 55m - 40m = 60f - 55f$

$\displaystyle \sf{ \implies } 15m = 5f$

$\displaystyle \sf{ \implies } f = 3m$

Hence the percentages of male students studying in the college

$\displaystyle \sf = \frac{m}{m + f} \times 100\%$

$\displaystyle \sf = \frac{m}{m + 3m} \times 100\%$

$\displaystyle \sf = \frac{m}{4m} \times 100\%$

$\displaystyle \sf = \frac{1}{4} \times 100\%$

$\displaystyle \sf =25\%$

∴ The percentages of male students studying in the college is 25%

Hence the correct option is d) 25%

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