Mixture and Alligation — Practice

Question 1

In what ratio must rice at ₹30/kg be mixed with rice at ₹40/kg to obtain a mixture worth ₹34/kg?
(a) 2:3 (b) 3:2 (c) 3:4 (d) 4:3

Accepted Answer

(b) 3:2.

Cross: (40 − 34):(34 − 30) = 6:4 = 3:2. More of the ₹30 rice, since 34 is nearer 30.

Question 2

A 40-litre mixture has milk and water in the ratio 3:1. The quantity of milk is:
(a) 25 L (b) 28 L (c) 30 L (d) 32 L

Accepted Answer

(c) 30 L.

Milk = 3/4 × 40 = 30 L, water = 10 L.

Question 3

60 litres of a mixture contains milk and water in the ratio 2:1. How much water must be added to make the ratio 1:1?
(a) 15 L (b) 20 L (c) 25 L (d) 30 L

Accepted Answer

(b) 20 L.

Milk = 40 L, water = 20 L. For 1:1, water must equal 40 L, so add 40 − 20 = 20 L.

Question 4

In what ratio must two varieties of pulses costing ₹15/kg and ₹20/kg be mixed to make a mixture worth ₹16.50/kg?
(a) 5:2 (b) 7:3 (c) 3:7 (d) 2:5

Accepted Answer

(b) 7:3.

Cross: (20 − 16.5):(16.5 − 15) = 3.5:1.5 = 7:3 (cheaper to dearer).

Question 5

From a vessel containing 40 litres of pure milk, 4 litres is drawn out and replaced with water. This is done twice. The milk now in the vessel is:
(a) 32 L (b) 32.4 L (c) 33.6 L (d) 34 L

Accepted Answer

(b) 32.4 L.

40 × (36/40)² = 40 × 0.81 = 32.4 L. The linear guess 40 − 2×4 = 32 ignores that the second draw removes some water too.

Question 6

In what ratio must water be mixed with milk so that selling the mixture at the cost price of the milk gives a 20% gain?
(a) 1:4 (b) 1:5 (c) 1:6 (d) 2:5

Accepted Answer

(b) 1:5.

The mixture must cost 1/1.2 = 5/6 of the milk price. Alligate water (0) and milk (1) to mean 5/6: (1 − 5/6):(5/6 − 0) = 1:5 (water:milk).

Question 7

The average weight of the boys in a class is 60 kg and of the girls 50 kg. The class average is 54 kg. The ratio of boys to girls is:
(a) 3:2 (b) 2:3 (c) 5:4 (d) 4:5

Accepted Answer

(b) 2:3.

Cross: boys:girls = (54 − 50):(60 − 54) = 4:6 = 2:3.

Question 8

A milkman sells milk at cost price but mixes water and thereby gains 25%. The ratio of water to milk in the mixture is:
(a) 1:4 (b) 1:5 (c) 1:3 (d) 4:1

Accepted Answer

(a) 1:4.

Selling at cost price, the gain equals water/milk. 25% = 1/4, so water:milk = 1:4.

Question 9

Vessel A has milk and water in ratio 4:1 and vessel B in ratio 3:2. Equal volumes from each are mixed. The milk-to-water ratio in the new mixture is:
(a) 7:3 (b) 3:2 (c) 5:3 (d) 2:1

Accepted Answer

(a) 7:3.

Milk fractions: A = 4/5, B = 3/5. Equal volumes → mean milk = (4/5 + 3/5)/2 = 7/10; water = 3/10. Ratio 7:3.

Question 10

In what ratio must sugar at ₹7/kg be mixed with sugar at ₹9/kg so that selling the mixture at ₹9.24/kg gives a 10% profit?
(a) 3:7 (b) 7:3 (c) 2:5 (d) 5:2

Accepted Answer

(a) 3:7.

Mixture cost = 9.24/1.1 = ₹8.40/kg. Cross: (9 − 8.4):(8.4 − 7) = 0.6:1.4 = 3:7 (cheaper ₹7 to dearer ₹9).

Practice — Mixture and Alligation

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