SSC CGL 2024 Tier-I · 13 September 2024, Shift 1 · Quantitative Aptitude · Question 10 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 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.

At a cafe, Rama bought drinks for her 7 friends at ₹240. Some of them wanted coffee, while others wanted black tea. A regular cup of coffee cost ₹40 and a regular cup of black tea cost ₹ 30. How many cups of tea did she purchase?

(a)5
(b)6
(c)3
(d)4

Answer

Why

Correct — D. Seven friends means 7 cups between them, and the whole bill is ₹240.

Let t = cups of black tea, so cups of coffee = 7 − t.
40(7 − t) + 30t = 240
280 − 10t = 240

10t = 40
t = 4 cups of tea → option (d)

Check: 3 coffees at ₹40 = ₹120 and 4 teas at ₹30 = ₹120, together ₹240.

Why the others are wrong

(a)
5 — 5 teas would leave only 2 coffees: 2 × 40 + 5 × 30 = ₹230, which is ₹10 short of the ₹240 actually spent.
(b)
6 — 6 teas with 1 coffee comes to 40 + 180 = ₹220 — twenty rupees below the bill, so the mix is too cheap.
(c)
3 — 3 is the number of coffees, not teas. Three teas with four coffees costs 160 + 90 = ₹250, ten rupees over.

Concept

Two unknowns, two conditions: a head count and a money total.

Because the count is fixed at 7, one substitution is enough — write the coffees as 7 − t and the cost equation has a single variable left.

The quicker classroom route is the assumption method. Suppose all 7 cups were coffee: that costs 7 × 40 = ₹280, which overshoots by ₹40. Each cup switched from coffee to tea saves ₹10, the price gap, so 40 ÷ 10 = 4 cups must be tea.

The stem says drinks for her 7 friends, so the cups number 7. It never says Rama drank anything herself.

Counting her in would make 8 cups, and ₹240 across 8 cups forces all eight to be tea at ₹30 — which the stem's 'some ... others' rules out, and which is not on the options anyway.

Key facts

The ₹240 bill splits as 3 cups of coffee at ₹40 and 4 cups of black tea at ₹30.
Swapping one coffee for one tea changes the bill by ₹10, the gap between the two prices.
All-coffee would cost ₹280, and the ₹40 excess divided by the ₹10 gap gives the 4 teas.

Study next

The assumption (alligation) method for two prices with a fixed total countTwo-variable linear equations built from a purchase totalCoin and ticket problems where both unknowns must be whole numbers

Common traps

Counting Rama herself and working with 8 cups instead of 7, which forces an all-tea bill that matches no option
Solving for the coffees and then reporting that number as the teas
Testing options and stopping at one that is close rather than exact

This is a two-price purchase with the head count fixed, so the whole item is one substitution or one alligation step.

Two-price blending also runs at Quant Q.5 of the same 13 Sep 2024, 09:00 paper, where rice at ₹250 per 5 kg and ₹280 per 5 kg is mixed in the ratio 7 : 8.

Related PYQs

No directly related past PYQ was found.