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1.  
How many kg of rice at ₹ 38 per kg must be mixed with 20 kg of rice at ₹ 53 per kg so that the mixture is worth ₹ 43 per kg?

Correct Answer: B [40 kg]

Explanation:

(53 − 43) : (43 − 38) = 10 : 5 = 2 : 1 → cheaper = 2 × 20 = 40 kg.

2.  
Two varieties of dal cost ₹ 60 and ₹ 75 per kg. The mixture is sold at ₹ 81 per kg at a profit of 20%. The mixing ratio is:

Correct Answer: A [1 : 1]

Explanation:

CP = 81 ÷ 1.2 = ₹ 67.50 → (75 − 67.5) : (67.5 − 60) = 1 : 1.

3.  
A drum holds 60 L of pure milk. 6 L is taken out and replaced with water; this is done twice in all. How much milk is now in the drum?

Correct Answer: C [48.6 L]

Explanation:

60 × (9/10)² = 60 × 0.81 = 48.6 L.

4.  
Two vessels contain milk and water in the ratios 3 : 2 and 5 : 3. Equal quantities are taken from both and mixed. The ratio of milk to water in the new mixture is:

Correct Answer: D [49 : 31]

Explanation:

Milk fractions 3/5 and 5/8 → average 49/80 → 49 : 31.

5.  
50 L of a mixture contains alcohol and water in the ratio 4 : 1. How much water must be added to make the ratio 2 : 3?

Correct Answer: E [50 L]

Explanation:

Alcohol 40 = 2 parts → 1 part = 20 → water must be 60; it is 10 → add 50 L.

6.  
A shopkeeper has 50 kg of wheat. He sells a part at 8% profit and the rest at 18% profit, making 14% profit overall. How many kg did he sell at 18% profit?

Correct Answer: B [30 kg]

Explanation:

Cross on profit %: (18 − 14) : (14 − 8) = 2 : 3 → 18% part = 3/5 × 50 = 30 kg.

7.  
Raghu travels 60 km in 5 hours, partly by cycle at 15 km/h and partly on foot at 5 km/h. How many km does he walk?

Correct Answer: C [7.5 km]

Explanation:

Average 12 km/h; times foot : cycle = (15 − 12) : (12 − 5) = 3 : 7 → 1.5 h on foot → 7.5 km.

8.  
Quantity I: Litres of milk in 45 L of a mixture with milk : water = 4 : 5.
Quantity II: Litres of water in 33 L of a mixture with milk : water = 5 : 6.

Correct Answer: A [Quantity I > Quantity II]

Explanation:

I: 4/9 × 45 = 20. II: 6/11 × 33 = 18.

9.  
How many litres of milk are there in the vessel?
I. The vessel holds 96 L of milk and water in the ratio 5 : 3.
II. The vessel has 36 L of water, which is 37.5% of the mixture.

Correct Answer: C [Either statement alone is sufficient]

Explanation:

I: 5/8 × 96 = 60 L. II: total = 36 ÷ 0.375 = 96 → milk 60 L.

10.  
Trick Spotter: which gives the ratio in which ₹ 30/kg and ₹ 50/kg pulses must be mixed to get a ₹ 36/kg mixture?

Correct Answer: B [(50 − 36) : (36 − 30)]

Explanation:

Cross Rule: cheaper : dearer = (d − m) : (m − c) = 14 : 6 = 7 : 3.

11.  
30 L of a mixture has milk and water in the ratio 7 : 3. Which of the following is/are correct?
I. Adding 5 L of water makes the ratio 3 : 2.
II. If 10 L of the mixture is taken out, 14 L of milk remains.
III. Adding 9 L of milk makes the ratio 3 : 1.

Correct Answer: C [Only I and II]

Explanation:

Milk 21, water 9. I: 21 : 14 = 3 : 2 ✓.

12.  
Alloy A has gold and copper in the ratio 7 : 2 and alloy B in the ratio 7 : 11. Equal weights of A and B are melted together. The ratio of gold to copper in the new alloy is:

Correct Answer: D [7 : 5]

Explanation:

Gold fractions 7/9 and 7/18 → average 7/12 → 7 : 5.

13.  
Reverse question: in what ratio must water be mixed with milk costing ₹ 48 per litre so that the mixture is worth ₹ 40 per litre?

Correct Answer: B [1 : 5]

Explanation:

Water costs ₹ 0: water : milk = (48 − 40) : (40 − 0) = 8 : 40 = 1 : 5.

14.  
In an office the average monthly salary is ₹ 30,000. The 30 officers average ₹ 48,000 and the other staff average ₹ 24,000. How many people work in the office?

Correct Answer: E [120]

Explanation:

Others : officers = (48 − 30) : (30 − 24) = 3 : 1 → others 90 → total 120.

15.  
Two qualities of ghee costing ₹ 70 and ₹ 90 per 100 g are mixed, and the mixture is sold at ₹ 76 per 100 g at a loss of 5%. The mixing ratio is:

Correct Answer: A [1 : 1]

Explanation:

CP = 76 × 100/95 = ₹ 80 → (90 − 80) : (80 − 70) = 1 : 1.

16.  
Three kinds of rice at ₹ 30, ₹ 36 and ₹ 45 per kg are mixed in the ratio 3 : 4 : 3. The price of the mixture per kg is:

Correct Answer: A [₹ 36.90]

Explanation:

(90 + 144 + 135) ÷ 10 = ₹ 36.90.

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