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
5111
A man buys milk at Rs. 5 per liter and after adding water sells it at Rs. 6 per liter, thereby making a profit of 33.33%. What is the proportion of water to milk?
Answer:
1:9
Step 1: CP = SP / (1+profit) = 6 / (4/3) = 4.5. Step 2: Alligate Water (0) and Milk (5) to get 4.5. Step 3: Ratio = 0.5 : 4.5 = 1 : 9.
5112
A mixture of 20 kg of spirit and water contains 10% water. How much water must be added to raise the percentage of water to 25%?
Answer:
4 kg
Step 1: Initial spirit = 90% of 20 = 18 kg. Step 2: Spirit stays 18 kg, which will be 75% of new mixture. Step 3: New volume = 18 / 0.75 = 24 kg. Water added = 24 - 20 = 4 kg.
5113
How much pure alcohol has to be added to 400 ml of a solution containing 15% alcohol to change the concentration to 32%?
Answer:
100 ml
Step 1: Alcohol = 15% of 400 = 60 ml. Step 2: Let x be pure alcohol added. (60 + x) / (400 + x) = 32/100 = 8/25. Step 3: 1500 + 25x = 3200 + 8x -> 17x = 1700 -> x = 100 ml.
5114
From a container of wine, a thief stole 15 liters of wine and replaced it with same quantity of water. He again repeated the same process. Thus, the ratio of pure wine and water becomes 343:169. What was the initial amount of wine in the container?
Answer:
120 liters
Step 1: Total parts = 343 + 169 = 512. Wine/Total = 343/512. Operations n=3. Step 2: (1 - 15/V)^3 = 343/512. Step 3: 1 - 15/V = 7/8 -> 15/V = 1/8 -> V = 120 liters.
5115
A 50 liter mixture of milk and water contains 10% water. How much water must be added to make the water 20% in the new mixture?
Answer:
6.25 liters
Step 1: Milk = 90% of 50 = 45L. Step 2: In the new mixture, water is 20%, so milk is 80%. Let new volume be V. 0.8V = 45 -> V = 56.25L. Step 3: Added water = 56.25 - 50 = 6.25 liters.
5116
In what proportion must a grocer mix sugar at Rs. 12/kg and Rs. 7/kg so as to make a mixture worth Rs. 8/kg?
Answer:
1:4
Step 1: Cheaper = 7, Dearer = 12, Mean = 8. Step 2: The question implies ratio of Dearer to Cheaper since 12 is stated first. Let's find Dearer:Cheaper = (8 - 7) : (12 - 8) = 1 : 4. Step 3: Ratio is 1:4.
5117
A trader mixes 26 kg of rice at Rs. 20 per kg with 30 kg of rice of another variety at Rs. 36 per kg and sells the mixture at Rs. 30 per kg. His profit percent is:
Answer:
5%
Step 1: Total CP = (26 * 20) + (30 * 36) = 520 + 1080 = 1600. Step 2: Total SP = 56 * 30 = 1680. Profit = 80. Step 3: Profit % = (80 / 1600) * 100 = 5%.
5118
If a milkman mixes water and milk in the ratio 1:5, what is the profit percentage if he sells the mixture at the cost price of pure milk?
Answer:
20%
Step 1: Water is the free additive. The profit comes entirely from the added water. Step 2: Profit % = (Water / Milk) * 100. Step 3: Profit % = (1/5) * 100 = 20%.
5119
Two vessels A and B contain spirit and water mixed in the ratio 5:2 and 7:6 respectively. Find the ratio in which these mixtures be mixed to obtain a new mixture containing spirit and water in the ratio 8:5.
Answer:
7:9
Step 1: Spirit in A = 5/7, in B = 7/13, target = 8/13. Step 2: Ratio = (8/13 - 7/13) : (5/7 - 8/13). Step 3: 1/13 : (65-56)/91 = 1/13 : 9/91 = 7 : 9.
5120
A liquid A is lighter than water by 20% and liquid B is heavier than water by 30%. In what ratio should they be mixed to get a mixture which is as heavy as water?
Answer:
3:2
Step 1: Let water weight be 100. A = 80, B = 130. Mean = 100. Step 2: Ratio of A to B = (130 - 100) : (100 - 80). Step 3: Ratio = 30 : 20 = 3 : 2.