Question

Rs 9,000 was divided equally among a certain number of people. Had there been 20 more people, each would have got Rs 160 less. Choose the correct statements.

• A. Original number of people was 20.
• B. Original number of people was 25.
• C. Increased number of people was 45.
• D. Increased number of people was 40.

Answer 1

Answer: (B), (C)

The correct options are
B

Original number of people was 25.

C

Increased number of people was 45.

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 = Rs 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,

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