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Question

P is x% more than Q. Q is (x - 10)% less than R. If P > R, what is the range of values x can take

CAT 2021

A
10% to 28%
CORRECT ANSWER WRONG ANSWER
B
10% to 25%
CORRECT ANSWER WRONG ANSWER
C
10% to 37%
CORRECT ANSWER WRONG ANSWER
D
10% to 43%
CORRECT ANSWER WRONG ANSWER
Solution

Correct option is

(C)

Explanatory Answer :

P = Q ( 1 + x/100)

Q = R ( 1 − (x−10)/100)

R = Q / ( 1 − (x−10)/100)

P > R

Q ( 1 + x/100) > Q / ( 1 − (x−10)/100)

1 + x/100 > 1 / (100−x+10/100)

100+x/100 > 100/110−x

(100 + x) (110 – x) > 100 * 100

11,000 + 110x – 100x – x^2 > 10000

1000 + 10x – x^2 > 0

x^2 – 10x – 1000 < 0

x^2 – 10x + 25 < 1000 + 25

(x – 5)^2 < 1025

x – 5 < 32

x < 37