All Categories MCQs
Topic Notes: All Categories
General Description
Plato
- Biography: Ancient Greek philosopher (427–347 BCE), student of Socrates and teacher of Aristotle, founder of the Academy in Athens.
- Important Ideas:
- Theory of Forms
- Philosopher-King
- Ideal State
5231
In what ratio must water be mixed with milk to gain 20% by selling the mixture at cost price?
Answer:
1:5
Step 1: Let the CP of 1 liter milk be Re. 1. SP of 1 liter mixture = Re. 1. Gain = 20%. Step 2: CP of 1 liter mixture = 1 / 1.20 = Rs. 5/6. Step 3: By alligation (Water CP = 0, Milk CP = 1, Mean CP = 5/6). Ratio of Water to Milk = (1 - 5/6) : (5/6 - 0) = 1/6 : 5/6 = 1 : 5.
5232
Milk and water in two vessels A and B are in the ratio 4:3 and 2:3 respectively. In what ratio, the liquids in both the vessels be mixed to obtain a new mixture in vessel C containing half milk and half water?
Answer:
7:5
Step 1: Proportion of milk in A = 4/7. In B = 2/5. In C (target) = 1/2. Step 2: Use alligation. Ratio = (1/2 - 2/5) : (4/7 - 1/2). Step 3: (5-4)/10 : (8-7)/14 = 1/10 : 1/14 = 14 : 10 = 7 : 5.
5233
A sum of Rs. 312 was divided among 100 boys and girls in such a way that each boy gets Rs. 3.60 and each girl Rs. 2.40. The number of girls is:
Answer:
40
Step 1: Average amount per student = 312 / 100 = Rs. 3.12. Step 2: Use alligation: Boys = 3.60, Girls = 2.40, Mean = 3.12. Step 3: Ratio of boys to girls = (3.12 - 2.40) : (3.60 - 3.12) = 0.72 : 0.48 = 3 : 2. Total parts = 5 = 100 students. Number of girls = (2/5) * 100 = 40.
5234
In what ratio must a grocer mix two varieties of tea worth Rs. 60 a kg and Rs. 65 a kg so that by selling the mixture at Rs. 68.20 a kg he may gain 10%?
Answer:
3:2
Step 1: Find the Cost Price (CP) of the mixture. SP = 68.20, Profit = 10%. CP = 68.20 / 1.10 = Rs. 62 per kg. Step 2: Use alligation with C = 60, D = 65, M = 62. Step 3: Ratio = (65 - 62) : (62 - 60) = 3 : 2.
5235
8 liters are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of the water is 16:65. How much wine did the cask hold originally?
Answer:
24 liters
Step 1: Let original volume be V. Total operations = 4. Final wine / Total volume = 16 / (16 + 65) = 16 / 81. Step 2: Formula: Final / Initial = (1 - R/V)^n. Step 3: 16 / 81 = (1 - 8/V)^4. Taking the fourth root: 2 / 3 = 1 - 8/V. 8/V = 1/3, so V = 24 liters.
5236
A mixture of 40 liters of milk and water contains 10% water. How much water must be added to make it 20% water in the new mixture?
Answer:
5 liters
Step 1: Initial water = 10% of 40 = 4L. Milk = 36L. Step 2: In the new mixture, water is 20%, so milk is 80%. Let total new volume be V. Step 3: 80% of V = 36L -> V = 36 / 0.8 = 45L. Added water = 45 - 40 = 5 liters.
5237
Find the ratio in which rice at Rs. 7.20 a kg be mixed with rice at Rs. 5.70 a kg to produce a mixture worth Rs. 6.30 a kg.
Answer:
2:3
Step 1: C = 5.70, D = 7.20, M = 6.30. Step 2: Since we are mixing 7.20 with 5.70, we find the ratio of D to C. Step 3: Ratio = (6.30 - 5.70) : (7.20 - 6.30) = 0.60 : 0.90 = 2 : 3.
5238
In what ratio must a grocer mix two varieties of pulses costing Rs. 15 and Rs. 20 per kg respectively to get a mixture worth Rs. 16.50 per kg?
Answer:
7:3
Step 1: C = 15, D = 20, M = 16.50. Step 2: Ratio = (20 - 16.50) : (16.50 - 15). Step 3: Ratio = 3.50 : 1.50 = 35 : 15 = 7 : 3.
5239
A mixture of a certain quantity of milk with 16 liters of water is worth Rs. 3 per liter. If pure milk is worth Rs. 7 per liter, how much milk is there in the mixture?
Answer:
12 liters
Step 1: Cost of water = Rs. 0. Cost of milk = Rs. 7. Mean cost = Rs. 3. Step 2: Ratio of water to milk = (7 - 3) : (3 - 0) = 4 : 3. Step 3: Quantity of water is 16 liters. Let milk be x. 4/3 = 16/x. Therefore, x = 12 liters.
5240
In what ratio must water be mixed with milk costing Rs. 12 per liter to obtain a mixture worth Rs. 8 per liter?
Answer:
1:2
Step 1: Cost of water is Rs. 0. Cost of milk is Rs. 12. Mean price is Rs. 8. Step 2: By alligation, Ratio = (12 - 8) : (8 - 0). Step 3: Ratio = 4 : 8 = 1 : 2.