In a company, all employees are getting equal wages. If the number of employees is increased by 20% and their wages per head are decreased by 18%, what is the percentage decrease in total wages?
- (a)1.6%
- (b)2.4%
- (c)1.4%
- (d)1%
Answer
Why
Correct — A. Total wages = number of employees × wage per head, so the two changes multiply.
Employees: × 1.20
Wage per head: × 0.82
Total wages: 1.20 × 0.82 = 0.984
0.984 of the original bill is a fall of 0.016, that is 1.6% → option (a)
By the successive-change formula: 20 + (−18) + (20 × −18) ⁄ 100 = 2 − 3.6 = −1.6%.
Why the others are wrong
- (b)2.4% — 2.4% would need 1.20 × 0.82 to come to 0.976. It comes to 0.984, which fixes the fall at 1.6%.
- (c)1.4% — 1.4% would need the product to be 0.986 rather than 0.984 — a single slip in the last digit of the multiplication, and the closest wrong answer on offer.
- (d)1% — 1% would need a product of 0.99. The product is 0.984, which fixes the fall at 1.6%. No reading of these two changes lands on a round 1%: with the cross term you get −1.6, without it a 2% rise.
Concept
Percentages attached to different bases cannot be added. Twenty per cent more employees and eighteen per cent less pay each act on the wage bill in turn, so the factors multiply.
Put numbers on it. Start with 100 employees at ₹100 each, a bill of ₹10,000. Afterwards there are 120 employees at ₹82 each, a bill of ₹9,840.
The fall is ₹160 on ₹10,000, which is 1.6%. Note that a naive 20 − 18 predicts a 2% rise, the opposite direction — the cross term is not a rounding detail here, it decides the sign.
The phrase 'all employees are getting equal wages' is what lets the bill be written as a simple product of headcount and rate.
Without it the 18% cut would have to be applied to a mix of different salaries, and the answer would depend on who was hired.
Key facts
- Total wages = employees × wage per head, so the two multipliers combine as 1.20 × 0.82 = 0.984.
- A drop from 1 to 0.984 is a decrease of 1.6%.
- Successive changes of a% and b% give a net change of a + b + ab⁄100 per cent, here 20 − 18 − 3.6 = −1.6.
- 100 employees at ₹100 cost ₹10,000, while 120 employees at ₹82 cost ₹9,840.
Study next
Common traps
- Adding the changes to get a 2% rise and dropping the cross term entirely.
- Applying both percentages to the same base, as though 20% were added to the bill and 18% taken off it.
- Taking the 18% cut off the new wage instead of the original wage per head.
SSC names two percentage changes on two quantities whose product is being asked about, so the work collapses to one multiplication once the structure is spotted.
The same successive-change move is set at 11 Sep 2024, 12:30, Quant Q.20, where a salary rises 25% and then falls 12%, and at 9 Sep 2024, 16:00, Quant Q.1, which chains a third change on top.
Related PYQs
No directly related past PYQ was found.