SSC CGL 2024 Tier-I · 10 September 2024, Shift 2 · Quantitative Aptitude · Question 17 of 100

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 6 September 2026.

Where this paper and its answers come from

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 merchant has 1000 kg of sugar, part of which he sells at a 10% profit and the rest at a 40% profit. He gains 20% on the whole. The quantity sold at 40% profit is:

Answer

Why

Correct — D. The options are pictures; option (d) shows 333⅓ kg.

Run alligation on the profit rates, with the overall 20% as the mean:
low rate = 10%, high rate = 40%, mean = 20%

quantity at 10% : quantity at 40% = (40 − 20) : (20 − 10)
= 20 : 10 = 2 : 1

So one part in three is sold at the higher margin:
1000 × 1⁄3 = 333⅓ kg → option (d).

Check it the long way: 0.10 × 666⅔ + 0.40 × 333⅓ = 66⅔ + 133⅓ = 200, which is 20% of 1000.

Why the others are wrong

(a)
383⅓ kg is the keyed figure nudged up by 50 — near enough to look plausible on a picture. Alligation fixes the split at exactly 2 : 1, and a third of 1000 kg is 333⅓.
(b)
443⅓ kg at the higher margin would drag the overall profit to about 23.3%, not 20%. A larger share at 40% pulls the average up, so the mean can no longer land on 20.
(c)
543⅓ kg puts more than half the stock at 40% profit, which lifts the overall gain to roughly 26.3%. Since 20 lies nearer 10 than 40, the 40% portion must be the smaller share.

Concept

Alligation is the weighted-average rule written as a ratio.

Two batches at 10% and 40% profit blend to an overall 20%. The distances from the mean set the split, and they set it inversely:
quantity at 10% : quantity at 40% = (40 − 20) : (20 − 10) = 2 : 1

The batch whose rate sits nearer the mean takes the larger share. 20 is 10 away from 10 but 20 away from 40, so twice as much sugar goes at the lower margin.

The rule works on any per-unit rate — price, concentration, speed, marks.

Alligation reads off directly in kilograms only because both parts of the stock share one cost price per kg. The weighting is really by cost, not by weight, and that unstated assumption is what lets the paper hand you the answer in kg.

Key facts

In alligation, quantity of the cheaper batch to quantity of the dearer batch is (dearer rate − mean) : (mean − cheaper rate).
Profit rates of 10% and 40% averaging to 20% split the stock 2 : 1 in favour of the 10% batch.
One third of 1000 kg is 333⅓ kg.
Alligation weights by cost price, so it converts straight into kilograms only when the cost per kg is the same for both parts.

Study next

Alligation applied to mixture concentrations and to average speedChecking an alligation ratio against the equation 0.1x + 0.4(1000 − x) = 200Repeated replacement of a mixture, where alligation is applied more than once

Common traps

Getting the ratio 2 : 1 right but attaching it to the wrong batch, which gives 666⅔ kg.
Treating the overall 20% as the midpoint of 10 and 40, which would be 25%.
Skimming the option images and missing the ⅓ that every choice carries.

Alligation is one line of arithmetic if you see it and a simultaneous equation if you do not. This shift also runs it on concentrations, where three acids at 20%, 30% and 40% are blended (10 Sep 2024, 12:30 PM, Quant Q.2).

Related PYQs

No directly related past PYQ was found.