Mrudula starts her job with a certain monthly salary and earns a fixed increment every year. If her salary was ₹28,400 after six years of service and ₹52,997 after fifteen years, find her annual increment.
- (a)₹1,824
- (b)₹12,002
- (c)₹1,200
- (d)₹2,733
Answer
Why
Correct — D. A fixed yearly increment makes the salary an arithmetic progression, so the rise between two years divides evenly by the years between them.
Years apart: 15 − 6 = 9
Total rise: 52,997 − 28,400 = ₹24,597
Annual increment: 24,597 ÷ 9 = ₹2,733
Check: 28,400 + 9 × 2,733 = 28,400 + 24,597 = ₹52,997 → option (d).
Why the others are wrong
- (a)₹1,824 — ₹1,824 adds only ₹16,416 over nine years, putting the fifteenth-year salary at ₹44,816 — some ₹8,000 short of the ₹52,997 the question states.
- (b)₹12,002 — ₹12,002 would add ₹1,08,018 over nine years, more than four times the ₹24,597 the salary actually rose.
- (c)₹1,200 — ₹1,200 covers a nine-year rise of just ₹10,800, which would leave the fifteenth-year salary at ₹39,200 rather than ₹52,997.
Concept
A salary with a fixed annual increment is an arithmetic progression: each year's pay is the previous year's plus a constant d.
Two properties make this a two-line problem. The difference between the pay of year m and year n is (m − n) × d, and the starting salary drops out of that subtraction entirely.
So Mrudula's first salary is never needed. Nine years separate the two figures given, and ₹24,597 ÷ 9 = ₹2,733 is the whole answer.
'After six years of service' can be read as the sixth term of the progression or the seventh, and candidates do argue about it.
It changes nothing here. On either reading the two salaries stand nine years apart, and only that gap enters the arithmetic.
Key facts
- With a constant increment, the salary difference between two years = (years between) × increment.
- 52,997 − 28,400 = 24,597, and 24,597 ÷ 9 = 2,733 exactly.
- The starting salary cancels in the subtraction, so it is never required.
Study next
Common traps
- Dividing the ₹24,597 rise by 15 instead of by the nine-year gap
- Hunting for the starting salary first, which the subtraction has already removed
A fixed step each year is the whole of this topic, whatever it is dressed as. The same arithmetic runs at 12 Sep 2024, 12:30, Quant Q.20 — 6 daisy plants gaining 3 a year against 26 jasmine plants losing 2 a year, equal after 4 years.
Whenever two years' figures are given and the starting figure is withheld, the gap between those years is the only number the subtraction needs.
Related PYQs
No directly related past PYQ was found.