SSC CGL 2024 Tier-I · 18 September 2024, Shift 2 · Quantitative Aptitude · Question 20 of 99

Text as printed on a candidate's response sheet for this shift; answer per SSC's tentative key as marked on that sheet. Solution last reviewed 10 September 2026.

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SSC does not publish CGL question papers or a public answer key. The questions and options here are reproduced as printed on a candidate's own response sheet for this shift — the Commission's text, unchanged. Each answer is SSC's tentative key as marked on that sheet; SSC allowed challenges to it and never publishes a final key. The solutions are written by UnlockIAS.

A total of ₹2,00,000 is divided into two parts for investing in different banks on simple interest. One yields 4% p.a. while the other yields 6% p.a. If the total interest at the end of one year is equivalent to 4.7% p.a. on the whole amount, the amount (in ₹) invested in each bank is ________, respectively.

(a)1,30,000 and 70,000
(b)1,20,000 and 80,000
(c)1,45,000 and 55,000
(d)1,60,000 and 40,000

Answer

Why

Correct — A. Total interest for the year = 4.7% of ₹2,00,000 = ₹9,400.

Let ₹x sit at 4% and ₹(2,00,000 − x) at 6%.
0.04x + 0.06(2,00,000 − x) = 9,400

12,000 − 0.02x = 9,400
0.02x = 2,600
x = ₹1,30,000 at 4%

The rest is 2,00,000 − 1,30,000 = ₹70,000 at 6% → option (a)

Alligation is quicker. The distances are 6 − 4.7 = 1.3 and 4.7 − 4 = 0.7, so the 4% part to the 6% part is 13 : 7, and 13⁄20 × 2,00,000 = ₹1,30,000.

Why the others are wrong

(b)
1,20,000 and 80,000 — Option (b), ₹1,20,000 and ₹80,000, earns 4,800 + 4,800 = ₹9,600. That is 4.8% of the whole, above the 4.7% given.
(c)
1,45,000 and 55,000 — Option (c), ₹1,45,000 and ₹55,000, earns 5,800 + 3,300 = ₹9,100, which works out at 4.55% overall.
(d)
1,60,000 and 40,000 — Option (d), ₹1,60,000 and ₹40,000, earns 6,400 + 2,400 = ₹8,800, or 4.4%. Too much money is parked at the lower rate.

Concept

A combined rate is a weighted average of the component rates, weighted by the money sitting at each.

Two consequences are usable before any algebra. The combined rate must lie strictly between the two component rates, and it lands nearer the rate carrying more money.

Here 4.7 is closer to 4 than to 6, so more than half the capital has to be at 4% — which already kills any split with under ₹1,00,000 at 4%.

Alligation turns that pull into a ratio: the two parts go as the opposite distances, (6 − 4.7) : (4.7 − 4) = 1.3 : 0.7 = 13 : 7.

Read the word respectively against the order in which the rates are named. The stem names 4% first, so the first figure in each option is the money invested at 4%.

Key facts

4.7% of ₹2,00,000 is ₹9,400, the interest the two parts must produce together in one year.
Alligation gives the lower-rate part to the higher-rate part as (higher − mean) : (mean − lower) = 1.3 : 0.7 = 13 : 7.
13⁄20 of ₹2,00,000 is ₹1,30,000 at 4%, leaving ₹70,000 at 6%.
A blended rate always lies strictly between the two rates being blended.

Study next

Alligation applied to mixtures of two prices or two concentrationsSimple interest split across two schemes with a stated combined returnDeciding which quantity a stated ratio attaches to before substituting

Common traps

Flipping the alligation ratio and putting ₹1,30,000 at 6%.
Assuming 4.7% implies a near-equal split, when an equal split would give exactly 5%.
Applying the 13 : 7 ratio to the interest instead of to the principal.

The same split-the-principal structure is set at 10 Sep 2024, 09:00, Quant Q.2, where ₹4,000 lent at 8% and 10% returns ₹352 in a year, and at 09 Sep 2024, 16:00, Quant Q.18, where two known deposits plus a total interest of ₹1,160 leave the rate on the remaining capital to be found.

Related PYQs

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