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Q45·CSAT · Prelims 2026

Quantitative — Mixture Allegation Systems

NumericalMixtures & AlligationArithmetic Problem● Easy

Question

An alloy P contains 20% copper and 80% zinc by weight. Another alloy Q contains 60% copper and 40% zinc by weight. A third alloy R is to be prepared from P and Q so that it contains equal amount of copper and zinc. In what ratio, amounts of P and Q be mixed in order to get R? [cite: 4484, 4485, 4486, 4487]

Options

a

1:3

Answer
b

3:1

c

2:3

d

3:2

Explanation

To find the mixing ratio of alloy P and alloy Q, apply a standard alligation framework focusing on the copper concentration across components [cite: 4484, 4485, 4486, 4487].

Component 1 (Alloy P): Copper concentration = 20\% = 0.20 .
Component 2 (Alloy Q): Copper concentration = 60\% = 0.60 .
Target Mixture (Alloy R): Requires equal amounts of copper and zinc, which means the target copper concentration is exactly 50\% = 0.50.
Apply the Alligation Cross Formula:
Cross difference 1 (Right side): |0.60 - 0.50| = 0.10
Cross difference 2 (Left side): |0.20 - 0.50| = 0.30
Calculate the Final Ratio:

Amount of P{Amount of Q} = 0.10/0.30 = 1/3

Thus, Alloy P and Alloy Q must be mixed in a 1:3 ratio to produce Alloy R.

Mixture problems targeting an equal balance are solved efficiently by finding the absolute differences between the initial concentrations and the 50% target value.

Answer: (a).

Question details

Year

2026

Paper

CSAT

Question

Q45

Section

Quantitative Aptitude

Sub-topic

Mixtures & Alligation

Type

Arithmetic Problem

Difficulty

Easy

Source hint

Alligations — two-component concentration balancing

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