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
111
A vessel contains 60 liters of pure milk. 6 liters are drawn and replaced by water. This is repeated once more. What percentage of original milk is left?
Answer:
81%
Each replacement removes 10% (6/60) of the milk. After 2 operations, fraction left = (1 - 10/100)^2 = 0.9^2 = 0.81. This is 81%.
112
10% of a mixture of sand and cement is sand. If 10 kg of sand is added to 40 kg of the mixture, what is the new percentage of sand?
Answer:
28%
Initial sand = 10% of 40 = 4 kg. Add 10 kg sand -> Total sand = 14 kg. New total mixture = 40 + 10 = 50 kg. Percentage = (14/50)*100 = 28%.
113
A sphere's radius is increased by 10%. Its volume increases by?
Answer:
33.1%
Volume depends on r^3. Multiplier is (1.10)^3 = 1.331. This means volume is 133.1% of original, an increase of 33.1%.
114
If the radius of a cylinder is decreased by 50% and height increased by 50%, what is the change in volume?
Answer:
62.5% decrease
Volume = pi * r^2 * h. New r = 0.5r. New h = 1.5h. New V = pi * (0.5r)^2 * (1.5h) = pi * 0.25r^2 * 1.5h = 0.375 * original V. Decrease is 1 - 0.375 = 0.625 or 62.5%.
115
The length and breadth of a rectangle are increased by 20% and 25% respectively. The percentage increase in area is?
Answer:
50%
Using successive formula: A + B + AB/100. 20 + 25 + (20*25)/100 = 45 + 500/100 = 45 + 5 = 50%.
116
The side of a square increases by 10%. The percentage increase in its perimeter is?
Answer:
10%
Perimeter is 4 * side. It is directly proportional to the side length. If side increases by 10%, perimeter also increases by 10%.
117
A solution of salt and water contains 5% salt by weight. If 20 liters of water evaporates and the solution now contains 15% salt, find the original quantity of solution.
Answer:
30 L
Salt remains constant. Let original quantity be x. 5% of x = 15% of (x - 20). 0.05x = 0.15x - 3. 0.10x = 3. x = 30 L.
118
Fresh fruit contains 68% water and dry fruit contains 20% water. How much dry fruit can be obtained from 100 kg of fresh fruit?
Answer:
40 kg
100 kg fresh fruit has 32% solid mass = 32 kg solid. Dry fruit has 20% water, so 80% is solid. Let total dry fruit be D. 80% of D = 32. D = 32 / 0.8 = 40 kg.
119
50 kg of an alloy of lead and tin contains 60% lead. How much lead must be melted into it to make the alloy contain 75% lead?
Answer:
30 kg
Initial lead = 30 kg, Tin = 20 kg. Add x kg lead. Tin remains 20 kg, which is now 25% of new total. 25% of Total = 20 -> Total = 80. New total = 50 + x = 80 -> x = 30 kg.
120
In a 40 L mixture of milk and water, 10% is water. How much water must be added to make water 20% of the new mixture?
Answer:
5 L
Initial water = 4 L, Milk = 36 L. Let added water be x. New total = 40+x. New water = 4+x. We want (4+x)/(40+x) = 0.20. Solving gives 4 + x = 8 + 0.2x. 0.8x = 4. x = 5 L.