SSC CGL 2025 Tier-I · 18 September 2025, Shift 2 · 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 person invested ₹20,000 in two different schemes. He invested one part for 4 years at 8% simple interest and the other part for the same duration at 10% simple interest. If the interest earned from the second part was ₹2,240 more than the interest earned from the first part, how much money was invested in the second scheme?

(a)₹8,000
(b)₹10,000
(c)₹12,000
(d)₹12,500

Answer

Why

Correct — C. Let the second part (10%) be ₹x, so the first part (8%) is ₹(20,000 − x).

Interest on the second: x × 10 × 4 ⁄ 100 = 0.4x
Interest on the first: (20,000 − x) × 8 × 4 ⁄ 100 = 6,400 − 0.32x
Set the difference: 0.4x − (6,400 − 0.32x) = 2,240

Open the bracket: 0.72x − 6,400 = 2,240
Add 6,400: 0.72x = 8,640
Divide by 0.72: x = ₹12,000

Check: 12,000 × 0.4 − 8,000 × 0.32 = 4,800 − 2,560 = ₹2,240
So the second scheme holds ₹12,000 → option (c).

Why the others are wrong

(a)
₹8,000 — ₹8,000 is the first part, the one at 8%. As the second part it would earn ₹3,200 against the first part's ₹3,840: ₹640 less, not ₹2,240 more.
(b)
₹10,000 — An equal split gives 10,000 × 0.4 = ₹4,000 against 10,000 × 0.32 = ₹3,200, a gap of only ₹800. The 10% part must be larger to open a ₹2,240 gap.
(d)
₹12,500 — ₹12,500 overshoots. The second part earns ₹5,000 and the first 7,500 × 0.32 = ₹2,400, a gap of ₹2,600 rather than ₹2,240.

Concept

Over 4 years, 10% simple interest earns 40% of a principal and 8% earns 32%.

Start with all ₹20,000 in the first part: it earns ₹6,400 and the second nothing, a gap of −6,400. Each rupee moved to the second part adds 0.40 there and removes 0.32 from the first, widening the gap by 0.72.

So 0.72x − 6,400 = 2,240, and x = 12,000.

The stem gives a difference of interests, not a total. That is why the two rates add (0.40 + 0.32) in the equation. A total-interest version would leave their difference (0.40 − 0.32 = 0.08) as the coefficient of x.

Key facts

Simple interest for 4 years is 40% of the principal at 10% and 32% at 8%.
₹12,000 at 10% for 4 years earns ₹4,800, and ₹8,000 at 8% for 4 years earns ₹2,560.
When the difference of the two interests is given, the coefficient of x is the sum of the two rate-time products: 0.40 + 0.32 = 0.72.

Study next

Splitting a sum when the total interest from both parts is givenSplits where the two parts run for different numbers of yearsAlligation on rates to split a sum by its average yield

Common traps

Marking ₹8,000, the amount in the first scheme, when the stem asks for the second.
Opening −(6,400 − 0.32x) as −6,400 − 0.32x instead of −6,400 + 0.32x, which wrecks the equation.

The total-interest version is asked 10 Sep 2024, 09:00, Quant Q.2 (₹4,000 at 8% and 10%, ₹352 a year, sum at 10% keyed ₹1,600) and 17 Sep 2025, 16:00, Quant Q.8 (₹15,000 at 10% and 12% for 3 years, ₹4,950 in all, amount lent to X keyed ₹7,500).

Related PYQs

No directly related past PYQ was found.

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