​₹9,000 is divided equally among a certain number of students. Had there been 20 more students each would have got ₹160 less. What was the original number of students?

Correct option is C

Given:

Total amount = ₹9,000

The amount received by each student in the original scenario =$$\frac{9000}{x}$$​,

where x is the original number of students.

The amount received by each student if 20 more students were added = $$\frac{9000}{x+20}$$​ ​, 

Solution:

From the given, we can form the equation:

​$$\frac{9000}{x} - \frac{9000}{x + 20} = 160$$​​

​$$\frac{9000}{x} - \frac{9000}{x + 20} = 160$$​​

​$$\frac{1}{x} - \frac{1}{x + 20} = \frac{160}{9000}$$​

​$$\frac{(x + 20) - x}{x(x + 20)} = \frac{16}{900}$$​​

​$$\frac{20}{x(x + 20)} = \frac{16}{900}$$​​

​$$20 \times 900 = 16 \times x(x + 20)$$​

​$$x^2 + 20x - 1125 = 0$$​​

x= $$\frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$​​

x = $$\frac{-20 \pm \sqrt{20^2 - 4(1)(-1125)}}{2(1)}$$​​

x =$$\frac{-20 \pm \sqrt{400 + 4500}}{2}$$​​

x=$$\frac{-20 \pm \sqrt{4900}}{2}$$​​

x =$$\frac{-20 \pm 70}{2}$$​​

x = $$\frac{-20 + 70}{2} = \frac{50}{2} = 25$$​​

or

x =$$\frac{-20 - 70}{2} = \frac{-90}{2} = -45$$​ $$\quad (\text{which is not possible})$$​​

The original number of students was 25.

Option (C) is right.