# Quantitative Reasoning – Practice – Percentages – Simplify questions using variable or work backwards from options!!!

PSA_LEVEL-UP_QNR28. The mass of two pieces of brasses is 60 kg. The first piece contains 10 kg of pure copper and the second 8 kg of pure copper. What is the percentage of copper in the first piece of brass if the percentage of copper in the second piece is 15 more than that in the first?

A) 20%
B) 30%
C) 25%
D) None of these

Ans:

Let the first piece be of ‘p’ kg and the second one of ’60-p’.

Percentage of copper in the first piece = 10*100/p
Percentage of copper in the second piece = 8*100/(60-p)

According to the question,
10*100/p = 8*100/(60-p) – 15
=>10/p – 8/(60-p) = -3/20
=>20[10(60-p) -8p] = -3p(60-p)
=>12000-360p] = -180p+3p2
=> 3p2 + 180p – 12000=0
=> p2 + 60p – 4000=0
=> p2 + 100p-40p – 4000=0
=>p=-100,40

Thus, possible value of p is 40 and the percentage of copper in the first piece of brass =10*100/40 = 25%. Option C.

Shortcut
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How to solve this from options working in a reverse manner!

Let us start with option A) 20% -> If the percentage of copper in the first piece of brass =20% or 10 kg, entire first brass weight = 10*5=50 kg. Thus, the second brass piece is of 10 kg weight and copper percentage = [8/10]*100 or 80%. This falsifies the condition of ‘15% difference’. Reject this option.

option B) 30% ->If the percentage of copper in the first piece of brass =30% or 10 kg, entire first brass weight = 10*10/3=100/3 kg. As soon as we see a non-integral value of the weight of the brass, we stop here! I know weight can be non-integral but let us check other options first. We will come back to this option after looking at rest other options.

option C) 25% -> If the percentage of copper in the first piece of brass =25% or 10 kg, entire first brass weight = 10*4=40 kg. Thus, the second brass piece is of 20 kg weight and copper percentage = [8/20]*100 or 40%. This SATISFIES the condition of ‘15% difference’. [25+15=40]. This is the correct option.

I suggest you try practising a lot of questions using different methods to arrive at the answer. This will bolster your confidence and give you a number of ways that sharpen your ‘art of solving’ aptitude questions. After all this is one of our laws of preparing for quantitative section of various aptitude examinations.