Percentage Q50

50.

A shopkeeper gives a discount of 12%, whereas a customer makes cash payment. Let 'p' denotes the percentage, above the cost price, that the shopkeeper must mark up the price of the articles ['p' is an integer] in order to make a profit of x% (x < 100). Which of the following is the possible value(s) of x?

	A.	54
	B.	76
	C.	96
	D.	32

Answer – (C)
Solution:
Let the cost price of one article is Rs r then:
Marked price of the article=r(1+p100)
Selling price =r(1+p100)(1−12100)
Profit percentage = x%
=> r(1+p100)(1−12100)=r(1+x100)
=> p=25(12+x)22
As, p is an integer, x must be multiple of 22.
All the possible values x, less than 100 are
k=10,32,54,76,98
Except option 'C' all the options are possible.