SSC CGL 2025 Tier-I · 16 September 2025, Shift 1 · Quantitative Aptitude · Question 9 of 100

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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A sum becomes ₹12100 in 2 years at 10% Compound Interest annually. Find the principal.

(a)₹10000
(b)₹11000
(c)₹11500
(d)₹10500

Answer

Why

Correct — A. Compound interest multiplies the sum by (1 + r⁄100) each year.

Yearly factor = 1 + 10⁄100 = 1.1
Two years: 1.1 × 1.1 = 1.21
Set up: P × 1.21 = 12100
Divide: P = 12100 ÷ 1.21 = ₹10000 → option (a)

Check: ₹10000 → ₹11000 after year 1 → ₹12100 after year 2

Why the others are wrong

(b)
₹11000 — ₹11000 is the amount after the first year. Dividing 12100 by 1.1 undoes only one year of growth, and the sum grew for two.
(c)
₹11500 — ₹11500 × 1.21 = ₹13915, well past ₹12100, so this principal is too large.
(d)
₹10500 — ₹10500 × 1.21 = ₹12705, which overshoots ₹12100 by ₹605.

Concept

With annual compounding, A = P(1 + r⁄100)ⁿ. To recover the principal, divide the amount by the growth factor: P = A ÷ (1 + r⁄100)ⁿ.

At 10% the factors are worth knowing by heart: 1.1 for one year, 1.21 for two, 1.331 for three. 12100 = 1.21 × 10000, so the principal comes out round.

Key facts

A = P(1 + r⁄100)ⁿ for interest compounded annually.
At 10% a year the growth factor is 1.21 over 2 years and 1.331 over 3 years.
Here the compound interest is 12100 − 10000 = ₹2100, against ₹2000 simple interest for the same 2 years.

Study next

CI − SI for 2 years = P(r⁄100)²Finding the rate from the amounts after n and n + 1 yearsHalf-yearly and quarterly compounding

Common traps

Dividing by 1.1 once, which returns the amount after one year (₹11000), not the principal.
Using simple interest: 12100 ÷ 1.2 ≈ ₹10083, which is not an option.

Amount, rate and time given, principal asked. The same 10% factor appears at 13 Sep 2025, 16:00, Quant Q.13, where ₹1,00,000 grows to ₹1,33,100 in 3 years, and a principal is recovered from two amounts at 12 Sep 2025, 09:00, Quant Q.11.

Related PYQs

No directly related past PYQ was found.

Topic: Interest — all 82 SSC CGL questions on it, every solved shift.