SSC CGL 2025 Tier-I · 17 September 2025, Shift 3 · Quantitative Aptitude · Question 8 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 11 September 2026.

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A man has ₹15,000. He lends a part of it to X for 3 years at 10% simple interest and the remaining to Y for 3 years at 12% simple interest. If the total interest received from both X and Y after 3 years is ₹4,950, find the amount lent to X.

(a)₹7,000
(b)₹7,500
(c)₹8,000
(d)₹8,500

Answer

Why

Correct — B. Both loans run for the same 3 years, so work with one year's interest.

Interest per year: 4,950 ÷ 3 = ₹1,650
Let X get ₹x at 10%, and Y get ₹(15,000 − x) at 12%

Interest: 0.10x + 0.12(15,000 − x) = 1,650
Expand: 0.10x + 1,800 − 0.12x = 1,650
Collect: 0.02x = 1,800 − 1,650 = 150
Divide by 0.02: x = ₹7,500 → option (b)

Why the others are wrong

(a)
₹7,000 — ₹7,000 to X leaves ₹8,000 to Y: 2,100 + 2,880 = ₹4,980 over 3 years, ₹30 more than ₹4,950.
(c)
₹8,000 — ₹8,000 to X leaves ₹7,000 to Y: 2,400 + 2,520 = ₹4,920 over 3 years, ₹30 short of ₹4,950.
(d)
₹8,500 — ₹8,500 to X leaves ₹6,500 to Y: 2,550 + 2,340 = ₹4,890 over 3 years, ₹60 short of ₹4,950.

Concept

The yearly interest fixes the average rate: 1,650 ÷ 15,000 = 11%.

11% sits exactly halfway between 10% and 12%, so by alligation the two parts are in the ratio (12 − 11) : (11 − 10) = 1 : 1. X and Y get ₹7,500 each.

The 3-year figures give the same answer. X's part earns 30% and Y's 36% over the period, and 0.30x + 0.36(15,000 − x) = 4,950 gives x = 7,500.

Key facts

Simple interest = principal × rate × time ⁄ 100.
When both parts run for the same time, divide the total interest by the time first.
When the average rate is midway between the two rates, the two parts are equal.

Study next

Splits where the two parts are lent for different timesFinding the rate when two sums earn a combined interestDividing a sum so that two compound-interest amounts become equal

Common traps

Treating ₹4,950 as one year's interest: 0.10x + 0.12(15,000 − x) = 4,950 gives a negative x, a sign the 3 years were left out.
Splitting the money 10 : 12 like the rates. The split comes from the distances to the 11% average, which are equal.

17 Sep 2025, 16:00, Quant Q.7 splits ₹5000 between 6% and 9% for one year: the 7.8% average gives 1.2 : 1.8 = 2 : 3, so ₹2000 is at 6%.

18 Sep 2025, 12:30, Quant Q.8 gives the difference of the interests instead: over 4 years, 0.40y − 0.32(20,000 − y) = 2,240, so 0.72y = 8,640 and the 10% part is ₹12,000.

Related PYQs

No directly related past PYQ was found.

Topic: Interest — all 58 SSC CGL questions on it, every solved shift.