SSC CGL 2025 Tier-I · 23 September 2025, Shift 3 · Quantitative Aptitude · Question 1 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 of money doubles itself at compound interest in 15 years. In how many years will it become eight times?

(a)45
(b)40
(c)42
(d)35

Answer

Why

Correct — A. Under compound interest the sum is multiplied by the same factor in every 15-year stretch.

Write the target as a power of 2: 8 = 2³
So the sum must pass through 3 doublings
Multiply by the doubling time: 3 × 15 = 45 years

Check: 15 years → ×2, 30 years → ×4, 45 years → ×8 → option (a)

Why the others are wrong

(b)
40 — At 40 years the sum has made only 40⁄15 = 2 2⁄3 doublings, about ×6.3, short of ×8. Whole doublings land at 15, 30 and 45 years.
(c)
42 — 42 years is 3 years short of the third doubling at 45 years, so the sum is still just under ×7, not ×8.
(d)
35 — At 35 years the sum is past ×4 (reached at 30 years), but the third doubling ends only at 45 years, so ×8 is still 10 years away.

Concept

Compound interest multiplies the amount by (1 + r⁄100) every year, so after n years the factor is (1 + r⁄100)ⁿ.

If that factor is 2 after 15 years, it is 2² = 4 after 30 years and 2³ = 8 after 45 years. You never need the rate itself.

In general, a sum that becomes k times in T years becomes kⁿ times in n × T years.

Doubling in 15 years implies roughly 4.7% a year compounded annually. Working with that decimal would only add rounding error; the power-of-2 ladder is exact.

Key facts

Under compound interest, if a sum becomes k times in T years, it becomes kⁿ times in nT years.
Eight times is 2³, so it takes three doubling periods: 3 × 15 = 45 years.
Under simple interest the growth is additive: a sum that doubles in 15 years needs 7 × 15 = 105 years to become eight times.

Study next

Finding the rate from a multiple: solve (1 + r⁄100)ⁿ = kTripling ladders: 3× in T years gives 9× in 2T and 27× in 3TSimple-interest multiples, where k times takes (k − 1) × the doubling time

Common traps

Treating the growth as simple interest and scaling by 8 − 1 = 7, which gives 105 years (not among the choices).
Counting 8 as four doublings because 8 = 4 × 2, which gives 60 years. The doublings run 2, 4, 8: there are three.

Here the doubling time is given and the multiple is a power of 2. The same ladder is asked at 12 Sep 2025, 09:00, Quant Q.10, where doubling in 5 years gives 8 times in 15 years.

At 22 Sep 2025, 09:00, Quant Q.1 the direction reverses: the multiple and the time are given and the rate is asked.

Related PYQs

No directly related past PYQ was found.

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