P is x% more than Q. Q is (x - 10)% less than R. If P R, what is the

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?

(A) 10% to 25%
(B) 10% to 28%
(C) 10% to 37%
(D) 10% to 43%
(E) 10% to 45%

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ankitgoswami · Answer

P = Q + x*Q/100

Q = R + (x-10)*R/100

And Remember P>R

So take only the upper values of the options given ie 25%, 28%, 37%, 43% & 45%

Now try with 25% first
P=1.25Q
Q=0.85R
So P=1.0625R
Holds true

Now let's jump to C, 37%
P=1.37 x 0.73R
P=1.0001R
Holds true

Now we know if we increase the value of x further then P will become less than R which will contradict the condition given.

Hence ans is  C

Aabiyeh · Answer

If the question said "Q is (x - 10)% less than R" then how come the equation "Q = R + (x-10)*R/100" is obtained. 
Can you please help me understand that.

if "Q" is less than R, then shouldn't we be adding in q to obtain some value of "R"?

Regor60 · Answer

That isn't correct.

Q = R  =

R - R(X-10)/100

"Q is 15% less than R" means

Q = R-R(15/100) = R

Posted from my mobile device

Aabiyeh · Answer

Thank You so much, and I think there is one more mistake. 
It is written Q=0.73R. If x = 37% then shouldn't Q=0.63R and hence P=0.8631R. Thus C can not be the right answer.
And even with x=28%, the answer is P=0.9216R.

Therefore the correct answer of this question should be option A and not C.

Please correct me if I am wrong.

samarpan.g28 · Answer

Firstly, P=Q{1+(x/100)}.
Secondly, Q=R{1-(x-10 /100)}.
Therefore, P=R{1-(x-10 /100)}{1+(x/100)}
or, P=R{11000+10x-x^2 / 10000}.
Given, P>R that means P/R>1.
When I put x=37 from option (C), P=1.0001R where 1.0001>1, so the correct option is (C). For x=25 and 28 also, P/R>1 but for x=37, it is the least value that satisfies the given condition. Further increasing x, the condition will not be satisfied.

I solved it using a calculator. Please let me know if there are any other methods to solve this.

P is x% more than Q. Q is (x - 10)% less than R. If P > R, what is the

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