Question

If the price of pen decreases by 20%, then a man can buy 10 more pens for rs 100. what is the new price (in rs) of each pen?

Answer 1

Let the number of pens brought originally be x and cost of each pen be y.

Therefor according to the question

x*y = 100               ............................(1)

and

(0.8*y)*(x + 10) = 100       .................(2)

by equation 2,
(0.8)*x*y + 8*y = 100

using equation 1,
(0.8)*(100)  +   8*y   =   100
8*y = 20
=>   y = 2.5

Therefore the new price is (0.8)*y = 0.8 * 2.5  = 2

The answer is Rs.2

Answer 2

Let the price of 1 pen initially be Rs. X
⇒ Number of pens he can buy now = 100/x
 After 20% discount price of 1 pen = x(1 – 20/100) = 0.8x
⇒ Number of pens he can buy now = 100/0.8x
According to problem statement,
⇒ 100/0.8x – 100/x = 10 pens
⇒ (100/x) × 1/4 = 10
⇒ x = 2.5
∴ the new price is 2.5 × 0.8 = Rs. 2