UPPSC PCS - 2015
If A’s monthly income is 40% more than that of B. how much percentage of B’s income is less than that of A ?
Year Asked: 2015
Detailed Explanation
Let B's income be 100. Then A's income is 140, since it is 40% more. The gap between them is 40, and the question asks what percentage of A's income B's shortfall represents. That is 40/140 × 100 = 28.57%, so the answer is C, assuming option C reads 28.57. The option text is missing in the question as given, which is why I am marking medium confidence.
Why the other options fail:
- A) 20 and D) 25 do not come from any correct reading of the ratio. They are close to 40/175 and 40/160 but not to 40/140.
- B) 28 is only a rounded value of 28.57. It is tempting, but a precise answer should carry the decimal.
Core concept: percentage change must be taken on the correct base. Here A is the reference, so the shortfall is divided by A, not by B. The same numbers give A being 40% more than B, which is a different figure from B being 28.57% less than A. This distinction is a recurring Quantitative Aptitude and data-interpretation point, and it shows up in Mains-style economic statistics too.
Trap: dividing 40 by 100 (B's base) and answering 40%, or stopping at the rounded 28 without checking whether the exact value is among the options.
This question appeared in UPPCS 2015 GS Paper 2.
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