Mathematics/General Ability MCQs
Topic Notes: Mathematics/General Ability
MCQs and preparation resources for competitive exams, covering important concepts, past papers, and detailed explanations.
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
161
How much pure alcohol has to be added to 400 ml of a solution containing 15% alcohol to change the concentration of alcohol in the mixture to 32%?
Answer:
100 ml
Step 1: Initial alcohol = 15% of 400 = 60 ml. Step 2: Let x ml of pure alcohol (100%) be added. Total alcohol = 60 + x. Total volume = 400 + x. Step 3: (60 + x) / (400 + x) = 32 / 100. 6000 + 100x = 12800 + 32x. 68x = 6800. x = 100 ml.
162
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 mixture be mixed to obtain a new mixture in vessel C containing spirit and water in the ratio 8:5.
Answer:
9:7
Step 1: Spirit in A = 5/7, in B = 7/13, Target in C = 8/13. Step 2: Alligation on spirit: Ratio = (8/13 - 7/13) : (5/7 - 8/13). Step 3: Ratio = 1/13 : (65-56)/91 = 1/13 : 9/91. Multiply by 91: 7 : 9. Wait, the ratio is (Target - B) : (A - Target) = (8/13 - 7/13) : (5/7 - 8/13) = 1/13 : 9/91 = 7/91 : 9/91 = 7:9. Correct option C. Let's re-read: ratio A:B = (Target - B) : (A - Target) = (8/13 - 7/13) : (5/7 - 8/13) = 1/13 : 9/91 = 7:9. Thus, ratio is 7:9.
163
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.
164
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.
165
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.
166
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.
167
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.
168
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.
169
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.
170
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.