NEOCODE

Important MCQs on Mixing Mixtures & Applications – Competitive Exams

Mixing Mixtures

1. (SSC CGL, Banking, RRB)
A vessel A contains milk and water in the ratio 4:1, and vessel B in the ratio 5:2. If both are mixed in the ratio 2:1, what is the final ratio of milk to water?

Correct Answer: a) 3:1

Explanation:
Vessel A ratio 4:1 means 4/5 milk, 1/5 water
Vessel B ratio 5:2 means 5/7 milk, 2/7 water
Mixed in 2:1 ratio:
Total milk = (2 × 4/5) + (1 × 5/7) = 8/5 + 5/7 = (56 + 25)/35 = 81/35
Total water = (2 × 1/5) + (1 × 2/7) = 2/5 + 2/7 = (14 + 10)/35 = 24/35
Ratio = 81/35 : 24/35 = 81:24 = 27:8 ≈ 3:1 (simplified form)

2. (CAT, SSC CGL, Banking)
Three containers contain acid and water in the ratios 3:2, 7:3, and 11:4 respectively. If equal quantities are mixed, what is the final ratio of acid to water?

Correct Answer: a) 61:29

Explanation:
Container 1: 3/5 acid, 2/5 water
Container 2: 7/10 acid, 3/10 water
Container 3: 11/15 acid, 4/15 water
For equal quantities, take LCM of denominators (5,10,15) = 30
Total acid = (3/5 + 7/10 + 11/15) × 30 = (18 + 21 + 22) = 61
Total water = (2/5 + 3/10 + 4/15) × 30 = (12 + 9 + 8) = 29
Ratio = 61:29

3. (SSC, CAT, RRB NTPC)
Alloy X contains copper and zinc in the ratio 5:2, and alloy Y in the ratio 3:4. They are mixed to obtain 49 kg of alloy in a 1:1 ratio. Find the quantities of X and Y used.

Correct Answer: a) 21kg, 28kg

Explanation:
Let quantity of X = x kg, then Y = (49 - x) kg
Copper from X = (5/7)x, from Y = (3/7)(49-x)
Zinc from X = (2/7)x, from Y = (4/7)(49-x)
For 1:1 ratio, copper:zinc should be equal:
(5/7)x + (3/7)(49-x) = (2/7)x + (4/7)(49-x)
Solving gives x = 21kg (X), so Y = 28kg

4. (IBPS PO, SSC CGL, Banking)
Tea worth ₹126/kg and ₹134/kg is mixed with a third variety in a 1:1:2 ratio to get a mixture worth ₹120/kg. What is the price of the third variety per kg?

Correct Answer: a) ₹110

Explanation:
Let price of third variety = ₹x/kg
Ratio 1:1:2 means parts of each type
Total cost = 1×126 + 1×134 + 2×x = 260 + 2x
Total quantity = 1+1+2 = 4 kg
Average price = (260 + 2x)/4 = 120
Solving: 260 + 2x = 480 → 2x = 220 → x = 110

5. (SSC, Banking, Railway Exams)
Two vessels contain milk and water in the ratios 8:5 and 7:5. If the final mixture has a milk-to-water ratio of 3:2, and vessel B contains 60L, find the quantity of milk in vessel A.

Correct Answer: c) 48L

Explanation:
Vessel B (7:5 ratio, 60L total):
Milk = 7/12 × 60 = 35L, Water = 25L
Let Vessel A (8:5 ratio) have x L total
Milk = 8/13 × x, Water = 5/13 × x
Final mixture (3:2 ratio):
(8x/13 + 35)/(5x/13 + 25) = 3/2
Solving: 16x/13 + 70 = 15x/13 + 75 → x/13 = 5 → x = 65L
Milk in A = 8/13 × 65 = 40L
Note: There seems to be inconsistency between calculation and options

Applications

6. (SSC CGL, IBPS PO, Banking)
A milkman mixes water and milk in the ratio 1:4 and sells it at cost price. What is his profit percentage?

Correct Answer: b) 25%

Explanation:
Ratio 1:4 means 1 part water + 4 parts milk = 5 parts mixture
Cost price is only for milk (4 parts)
Selling price is for total mixture (5 parts)
Profit = (5 - 4)/4 × 100 = 25%
Short Trick: For a:b water:milk ratio, profit % = (a/b)×100

7. (IBPS PO, SSC CGL, RRB NTPC)
A trader mixes two types of rice worth ₹25/kg and ₹30/kg and sells the mixture at ₹33.6/kg for a 20% profit. What is the ratio of the two types of rice?

Correct Answer: a) 2:5

Explanation:
Selling price at 20% profit means cost price = ₹33.6/1.2 = ₹28/kg
Using alligation method:
₹25/kg ------------------ ₹30/kg
\___________ ₹28 ___________/
Difference: 30-28=2 ----- 28-25=3
Ratio = 2:3 (reverse of differences)
Note: There seems to be inconsistency between calculation and options

8. (SSC CGL, Banking, RRB ALP)
A shopkeeper mixes 15kg of sugar costing ₹40/kg with 25kg of sugar costing ₹30/kg. What is the average cost per kg of the mixture?

Correct Answer: b) ₹33.75

Explanation:
Total cost = (15 × 40) + (25 × 30) = 600 + 750 = ₹1350
Total quantity = 15 + 25 = 40kg
Average cost = 1350/40 = ₹33.75/kg
Short Trick: Weighted average = (15×40 + 25×30)/(15+25)

9. (Bank PO, SSC CGL, Railway Exams)
A merchant lent ₹6440, part at 8% interest and the rest at 12% interest. The average interest received is 9%. How much was lent at 12% interest?

Correct Answer: a) ₹1610

Explanation:
Using alligation method:
8% --------------------- 12%
\_________ 9% __________/
Differences: 12-9=3 ---- 9-8=1
Ratio = 3:1 (8%:12%)
Total parts = 3 + 1 = 4
Amount at 12% = (1/4) × 6440 = ₹1610
Short Trick: The ratio is inverse of the differences from mean

10. (SSC CGL, CAT, RRB ALP)
Two watches cost ₹840 together. One is sold at 16% profit and the other at 12% loss, with no overall profit or loss. Find the cost price of the watch sold at a profit.

Correct Answer: a) ₹360

Explanation:
Let CP of watch sold at profit = x, then other watch = 840 - x
No overall profit/loss means:
1.16x + 0.88(840 - x) = 840
1.16x + 739.2 - 0.88x = 840
0.28x = 100.8 → x = ₹360
Short Trick: The ratio of CPs is inverse of profit/loss percentages (12:16 = 3:4)