CSAT Solved Papers/ 2022/Q20

2022 CSAT — Q20

Quant Arithmetic & numeracy 2.5 marks Easy

The increase in the price of a certain item was $25\%$ . Then the price was decreased by $20\%$ and then again increased by $10\%$ . What is the resultant increase in the price?

A 5%
B 10% Answer
C 12.5%
D 15%

Worked rationale

Chain the multipliers — never add the percentages:

1.25 \times 0.80 \times 1.10 = (1.25 \times 0.80) \times 1.10 = 1.00 \times 1.10 = 1.10.

A net multiplier of $1.10$ means a $10\%$ increase.

Answer: (b) 10%.

Why the other options miss

A

added the signed changes: combines $+25 - 20 + 10$ and then mishandles, or nets a wrong combination.
C

an arithmetic slip: mis-multiplies (e.g. $1.25 \times 0.9$ ) or averages two of the steps.
D

treated the percentages as additive: naively sums $+25 - 20 + 10 = 15$ instead of multiplying the factors.

Specialist insight

The engineered trap is the additive answer $+25-20+10 = 15\%$ (option d). Successive percentage changes multiply, and here the first two cancel exactly ( $1.25 \times 0.80 = 1$ ), leaving just the final $\times 1.10$ . Spotting that $25\%$ up then $20\%$ down returns to the original is the one-line shortcut.

The trap, in one line

$1.25 \times 0.80 = 1$ , so only the final $\times 1.10$ survives $\Rightarrow 10\%$ , not the additive $15\%$ $=$ (b).

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