Question

A sum of ₹ 9,000 was divided equally among a certain number of people. If there are 20 more people, each would have got Rs. 160 less. Find the original number of people.

• A. 25
• B. 24
• C. 26
• D. 27

Answer 1

The correct option is A 25

Let the original number of people be x and the increased number of people be y.
According to the question y = x + 20 ...(1)
Total amount = ₹9000

The original share each person gets
$=\frac{Totalamount}{Numberofpeople}=\frac{9000}{x}$
The share of each person after increasing the number of people
= $\frac{9000}{y}$
Original share of each person - share of each of the increased persons = Rs 160
$\Rightarrow \frac{9000}{x}-\frac{9000}{y}=160$

Dividing both sides by 40, we get,
$\frac{225}{x}-\frac{225}{y}=4$ ...(2)

Putting y = x + 20 from equation (1) in equation (2) we get,

$\Rightarrow \frac{225}{x}-\frac{225}{x+20}=4$

$\Rightarrow \frac{225x+4500-225x}{x(x+20)}=4\Rightarrow \frac{4500}{x(x+20)}=44x^2+80x=4500\Rightarrow x^2+20x=1125\Rightarrow x^2+20x-1125=0\Rightarrow x^2+45x-25x-1125=0\Rightarrow x(x+45)-25(x+45)=0\Rightarrow (x-25)(x+45)=0\Rightarrow x=25orx=-45$
But, number of people cannot be negative.
Hence, the original number of people is 25.