CSAT Solved Papers/ 2024/Q16

2024 CSAT — Q16

Quant Arithmetic & numeracy 2.5 marks Medium

What percent of water must be mixed with honey so as to gain 20%20\% by selling the mixture at the cost price of honey?

  1. A 20% Answer
  2. B 10%
  3. C 5%
  4. D 4%

Worked rationale

Water is free; honey costs money. Take 1 litre of honey at cost ₹11 per litre (a convenient anchor), and add ww litres of water (cost 00).

  • Cost of the mixture == ₹11 (only the honey cost anything).
  • Mixture volume =(1+w)= (1 + w) litres.
  • It is sold at the cost price of honey, i.e. ₹11 per litre, so revenue =(1+w)×1== (1+w)\times 1 = ₹(1+w)(1+w).

Profit =(1+w)−1=w= (1+w) - 1 = w on a cost of 11, so gain %=100w\% = 100w. Set equal to 20%20\%:

100w=20 ⇒ w=0.2 litre of water per 1 litre of honey=20%.100w = 20 \ \Rightarrow\ w = 0.2 \text{ litre of water per 1 litre of honey} = 20\%.

Answer: (a) 20%.

Visual solution

The same solve, worked by hand — read it, then trace it.

Hand-drawn worked solution for UPSC 2024 CSAT Q16 — Arithmetic & numeracy
Tap the drawing to open it full size for the fine detail.

Why the other options miss

  • B
    the wrong base: applies the gain on the selling/total volume instead of on cost, e.g. treats 20%20\% as profit on the mixture and solves w1+w=0.2⇒w=0.25\tfrac{w}{1+w}=0.2\Rightarrow w=0.25 then mis-reduces, or simply halves 20%20\% on a wrong-base instinct.
  • C
    an arithmetic slip: inverts the relationship (20%20\% gain →120=5%\to \tfrac{1}{20}=5\% water), a reflexive “take the reciprocal” error.
  • D
    two wrong steps stacked: combines 15\tfrac{1}{5} of 15\tfrac{1}{5}, or 20%20\% of 20%20\% — landing on 4%4\%.

Specialist insight

The whole class of “adulterate with a free component, sell at the pure price” problems reduces to one line: the gain percent equals the fraction of free stuff added, measured against the paid stuff. Selling the diluted mixture at honey’s price means every drop of water is pure profit. So 20%20\% gain ⇔\Leftrightarrow 20%20\% of the honey’s volume is water — no equations needed once you see it. The trap is the base: profit is on cost (the honey), not on the mixture volume, so it is waterhoney\tfrac{\text{water}}{\text{honey}}, not waterhoney+water\tfrac{\text{water}}{\text{honey}+\text{water}}. Anchor the honey at 11 litre / ₹11 and the arithmetic disappears. (This is the same engine as “milkman adds water”; recognise the template and it’s a 30-second item.)

The trap, in one line

Profit is measured on the cost (the honey), so water =20%= 20\% of honey — not w1+w\tfrac{w}{1+w} of the mixture.

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