Question

By selling a pen for Rs. 165, mukti gains 10%. If she had sold it for Rs. 157.50, what percentage would she have lost or gained?

Answer 1

let initial amount be x then after 10% gain it will be

x+10%x=165
x+1/10x  = 165
11/10x=165
x=165(10/11)
x=15(10)
x=150

let the percentage be y
y% of 150 + 150 = 157.50
y%150=7.50
y=7.50(100/150)
y=7.50(2/3)
y=2.5*2
y=5

therefore the percentage of gain after selling pen at 157.50 is 5%

ANS=>   5%

hope this helps you 

Reguards 
Vishwas Choudhary

Answer 2

Let the cost price of pen = x
for selling at Rs. 165, profit = 10%

So x+10% of x = 165
⇒x + 10x/100 = 165
⇒x + 0.1x = 165
⇒1.1x = 165
⇒x = 165/1.1 = Rs. 150

now if he sells at Rs. 157.50
profit = 157.5-150 = Rs. 7.5
in percentage = (7.5/150)×100 = 5%
She would gain 5% by selling it for Rs. 157.50.