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1.  
In what ratio must rice at ₹ 40 per kg be mixed with rice at ₹ 55 per kg to get a mixture worth ₹ 45 per kg?

Correct Answer: D [2 : 1]

Explanation:

Cross Rule: (55 − 45) : (45 − 40) = 10 : 5 = 2 : 1.

2.  
60 L of a mixture contains milk and water in the ratio 3 : 1. The quantity of milk is:

Correct Answer: B [45 L]

Explanation:

3/4 × 60 = 45 L.

3.  
20 L of a 30% acid solution is mixed with 30 L of a 40% acid solution. The strength of the mixture is:

Correct Answer: C [36%]

Explanation:

Acid = 6 + 12 = 18 L in 50 L → 36%.

4.  
45 L of milk and water are in the ratio 4 : 1. How much water must be added to make the ratio 3 : 2?

Correct Answer: A [15 L]

Explanation:

Milk 36 = 3 parts → 1 part = 12 → water must be 24; it is 9 → add 15 L.

5.  
4 kg of sugar at ₹ 45 per kg is mixed with 6 kg at ₹ 60 per kg. The price of the mixture per kg is:

Correct Answer: A [₹ 54]

Explanation:

(180 + 360) ÷ 10 = ₹ 54.

6.  
True or false? "Taking out some mixture from a vessel does not change the ratio of the ingredients left in it."

Correct Answer: D [True]

Explanation:

Every ingredient falls in the same proportion, so the ratio is unchanged.

7.  
Fill in the blank: Equal quantities of tea at ₹ 120 and ₹ 180 per kg are mixed. The mixture is worth ₹ ____ per kg.

Correct Answer: B [150]

Explanation:

Equal quantities → simple average (120 + 180)/2 = 150.

8.  
Odd one out – which milk : water ratio does NOT give a mixture that is 60% milk?

Correct Answer: C [4 : 3]

Explanation:

4 : 3 → 4/7 ≈ 57.1%; the others are 3/5 = 60%.

9.  
Match the milk : water ratio with the percentage of milk: (i) 3 : 1 (ii) 1 : 4 (iii) 2 : 3 (iv) 7 : 3 ; (p) 20% (q) 40% (r) 75% (s) 70%

Correct Answer: A [i-r, ii-p, iii-q, iv-s]

Explanation:

3/4 = 75%, 1/5 = 20%, 2/5 = 40%, 7/10 = 70%.

10.  
A 12% sugar solution and a 36% sugar solution are mixed to get a 20% solution. The ratio of the 12% solution to the 36% solution is:

Correct Answer: B [2 : 1]

Explanation:

(36 − 20) : (20 − 12) = 16 : 8 = 2 : 1.

11.  
A milkman buys milk at ₹ 40 per litre, mixes water with it in the ratio water : milk = 1 : 4, and sells the mixture at ₹ 40 per litre. His gain is:

Correct Answer: D [25%]

Explanation:

1 L of mixture costs him 4/5 × 40 = ₹ 32; sells at ₹ 40 → 8/32 = 25%.

12.  
In a class, 25 boys have an average mark of 52 and 15 girls have an average mark of 60. The average mark of the class is:

Correct Answer: C [55]

Explanation:

(1,300 + 900) ÷ 40 = 55.

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