CSAT Solved Papers/ 2021/Q78

2021 CSAT — Q78

Quant Arithmetic & numeracy 2.5 marks Easy

If the price of an article is decreased by $20\%$ and then the new price is increased by $25\%$ , then what is the net change in the price?

A 0% Answer
B 5% increase
C 5% decrease
D Cannot be determined due to insufficient data

Worked rationale

Apply the changes as multipliers on the original price:

\text{net multiplier} = (1 - 0.20)\times(1 + 0.25) = 0.80 \times 1.25 = 1.00.

The final price equals the original, so the net change is $0\%$ .

Answer: (a) 0%.

Why the other options miss

B

added the percentages: does $-20\% + 25\% = +5\%$ instead of multiplying the factors.
C

wrong base: applies the $25\%$ rise to the original price, not the reduced one.
D

thought a real price was needed: misses that successive percentages give a fixed multiplier.

Specialist insight

Successive percentage changes multiply, never add — the whole trap is the $-20\%$ then $+25\%$ looking like a net $+5\%$ . The factors $0.8\times 1.25 = 1$ exactly because $1.25 = 1/0.8$ , so the rise perfectly undoes the fall. You never need a real price: chain the multipliers and read off the net factor. Whenever a fall of $a\%$ is followed by a rise of $\dfrac{a}{1-a/100}\%$ , the result is back to the start.

The trap, in one line

$0.8 \times 1.25 = 1.0$ (multiply, don't add), so net change $= 0\% \Rightarrow$ (a).

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