A number is first increased by 12% and then increased by 23%. The number, so obtained, is now decreased by 34%. What is the net increase or decrease percent in the original number (nearest to an integer)?
- (a)9% increase
- (b)10% decrease
- (c)9% decrease
- (d)10% increase
Answer
Why
Correct — C. Successive percentage changes multiply, so chain the factors instead of adding the numbers.
+12% → ×1.12
+23% → 1.12 × 1.23 = 1.3776
−34% → 1.3776 × 0.66 = 0.909216
The final value is 0.909216 of the original, so the change is 0.909216 − 1 = −0.090784.
That is a fall of 9.08%, which to the nearest integer is a 9% decrease → option (c).
Why the others are wrong
- (a)9% increase — The sign is the miss. The overall factor 0.909216 is below 1, so the number ends smaller than it started — 9.08 is the right size but the wrong direction.
- (b)10% decrease — Over-rounding. The exact factor is 0.909216, a fall of 9.08%, and 9.08 rounds to 9, not to 10. Squashing 0.909 to 0.90 is what produces this figure.
- (d)10% increase — Two errors at once — the direction is down, not up, and the size is 9.08, not 10. Neither half of this option survives the multiplication.
Concept
Percentage changes applied one after another multiply; they never add.
Each change rescales whatever the previous step produced, so a p% change becomes the factor (1 + p⁄100): +12% is ×1.12, −34% is ×0.66.
The net factor is the product of the individual factors, and the net change is that product minus 1.
Adding 12 + 23 − 34 gives +1%, which is nowhere near the truth: the 23% is charged on a number already 12% bigger, and the 34% is taken off a number bigger still.
The stem's rider "nearest to an integer" is a warning that the exact figure will not be tidy — here it is 9.0784%, so a candidate who arrives at a round number has almost certainly added instead of multiplied.
Key facts
- Two successive changes of p% and q% combine into a single change of p + q + pq⁄100 percent.
- The first two changes here combine to 12 + 23 + (12×23)⁄100 = 37.76%, a factor of 1.3776.
- A 34% fall is the factor 0.66, and 1.3776 × 0.66 = 0.909216 — a net fall of 9.08%.
- A net factor below 1 always means a decrease, whatever the individual steps were.
Study next
Common traps
- Adding 12 + 23 − 34 to get +1%, because successive percentages do not add.
- Rounding the factor 0.909216 to 0.90 and answering 10%.
- Reading a factor below 1 as an increase.
SSC frames this as two or three chained changes with a "nearest to an integer" rider, which is itself a hint that the exact multiplier is untidy.
Percentage arithmetic also runs Quant Q.17 (a dishonest shopkeeper's effective profit), Quant Q.20 (a discount percentage) and Quant Q.24 (a percentage rise read off a table).
Related PYQs
No directly related past PYQ was found.