SSC CGL 2025 Tier-I · 17 September 2025, Shift 1 · Quantitative Aptitude · Question 7 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 ₹10000 is lent out in two parts, one at 7% simple interest and the other at 12% simple interest. If the annual interest is ₹900, the sum lent at 12% is:

(a)₹3500
(b)₹4000
(c)₹4500
(d)₹5000

Answer

Why

Correct — B. Let the sum at 12% be ₹x, so ₹(10000 − x) earns 7%.

Interest for one year: 0.12x + 0.07(10000 − x) = 900
Expand: 0.12x + 700 − 0.07x = 900
Collect: 0.05x = 200
Divide: x = 200 ÷ 0.05 = 4000

The sum at 12% is ₹4000 → option (b)

Why the others are wrong

(a)
₹3500 — ₹3500 at 12% earns ₹420, and ₹6500 at 7% earns ₹455. The total, ₹875, is ₹25 short of ₹900.
(c)
₹4500 — ₹4500 at 12% earns ₹540, and ₹5500 at 7% earns ₹385. The total, ₹925, is ₹25 more than ₹900.
(d)
₹5000 — ₹5000 in each part earns ₹600 + ₹350 = ₹950, ₹50 over. An even split needs an average rate of 9.5%, and here it is 9%.

Concept

Alligation is the fast route. The whole ₹10000 earns ₹900, an average rate of 9%.

Each part gets the distance of the other rate from the average: the 7% part gets 12 − 9 = 3, the 12% part gets 9 − 7 = 2. So 7% part : 12% part = 3 : 2.

The 12% part is 2⁄5 of ₹10000 = ₹4000, matching the equation.

A third route: all ₹10000 at 7% would earn ₹700. Each rupee moved to 12% adds 5 paise, so the extra ₹200 needs ₹200 ÷ 0.05 = ₹4000 at 12%.

Key facts

Average rate = total interest ÷ total sum × 100, here 900 ÷ 10000 × 100 = 9%.
Alligation: lower-rate part : higher-rate part = (higher rate − average) : (average − lower rate).
Simple interest for one year = principal × rate ⁄ 100.

Study next

Alligation for mixtures at two pricesSums lent at two rates for different periodsAverage rate of return on a split investment

Common traps

Reading the alligation ratio the wrong way round. 3 : 2 is 7% part to 12% part, and flipping it puts ₹6000 at 12%.
Taking the average of the two rates, 9.5%, instead of the actual average rate, 900 ÷ 10000 = 9%.

17 Sep 2025, 16:00, Quant Q.7 is the same frame: ₹5000 at 6% and 9% earning ₹390 is an average of 7.8%, so the parts are 1.2 : 1.8 = 2 : 3 and ₹2000 sits at 6%. 18 Sep 2024, 12:30, Quant Q.20 splits ₹2,00,000 at 4% and 6% the same way.

Related PYQs

No directly related past PYQ was found.

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