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
221
If a : b = c : d = e : f = 1 : 2, then (3a + 5c + 7e) : (3b + 5d + 7f) is equal to:
Answer:
1 : 2
Since a/b = c/d = e/f = 1/2, we have a = b/2, c = d/2, and e = f/2. Substituting these into the numerator: 3(b/2) + 5(d/2) + 7(f/2) = 0.5 * (3b + 5d + 7f). The ratio of numerator to denominator is 0.5, which is 1 : 2.
222
The ratio of the length and breadth of a rectangular field is 5 : 4. If the breadth is 20 meters less than the length, the perimeter of the field is:
Answer:
360 m
Let length be 5x and breadth be 4x. Difference = 5x - 4x = x. Given x = 20 m. Length = 100 m, breadth = 80 m. Perimeter = 2 * (L + B) = 2 * (100 + 80) = 2 * 180 = 360 m.
223
Find the fraction which bears the same ratio to 1/27 that 3/11 does to 5/9.
Answer:
1/55
Let the fraction be x. x : (1/27) = (3/11) : (5/9). So, x / (1/27) = (3/11) / (5/9). 27x = (3/11) * (9/5) = 27/55. Dividing both sides by 27 gives x = 1/55.
224
The incomes of A and B are in the ratio 3 : 2 and their expenditures are in the ratio 5 : 3. If each saves Rs. 1000, A's income is:
Answer:
Rs. 6000
Let incomes be 3x and 2x, and expenditures be 5y and 3y. 3x - 5y = 1000 and 2x - 3y = 1000. Equating them: 3x - 5y = 2x - 3y => x = 2y. Substitute x in the first equation: 3(2y) - 5y = 1000 => y = 1000. So x = 2000. A's income = 3x = Rs. 6000.
225
Two numbers are in the ratio 5 : 9. If 9 is added to each, they are in the ratio 16 : 27. The second number is:
Answer:
99
Let numbers be 5x and 9x. (5x + 9) / (9x + 9) = 16 / 27. Cross-multiplying: 27(5x + 9) = 16(9x + 9) => 135x + 243 = 144x + 144 => 9x = 99 => x = 11. The second number is 9x = 9 * 11 = 99.
226
A sum of money is distributed among A, B, C, and D in the ratio 5 : 2 : 4 : 3. If C gets Rs. 1000 more than D, what is B's share?
Answer:
Rs. 2000
Let the shares be 5x, 2x, 4x, and 3x. C's share - D's share = 4x - 3x = x. We are given x = 1000. B's share is 2x = 2 * 1000 = Rs. 2000.
227
If 10% of x is the same as 20% of y, then x : y is equal to:
Answer:
2 : 1
10% of x = 20% of y translates to 0.1x = 0.2y. Multiply both sides by 10 to get x = 2y. Therefore, the ratio x / y = 2 / 1, which is 2 : 1.
228
The ratio of two numbers is 3 : 8, and their difference is 115. The larger number is:
Answer:
184
Let the numbers be 3x and 8x. Their difference is 8x - 3x = 5x. Given 5x = 115, solving gives x = 23. The larger number is 8x = 8 * 23 = 184.
229
In a mixture of 45 liters, the ratio of milk and water is 4 : 1. How much water must be added to make the mixture ratio 3 : 2?
Answer:
15 liters
Initial Milk = (4/5) * 45 = 36 L. Initial Water = (1/5) * 45 = 9 L. Let x liters of water be added. New ratio: 36 / (9 + x) = 3 / 2. Cross-multiplying: 72 = 27 + 3x => 3x = 45 => x = 15 L.
230
Seats for Mathematics, Physics, and Biology in a school are in the ratio 5 : 7 : 8. There is a proposal to increase these seats by 40%, 50%, and 75% respectively. What will be the ratio of increased seats?
Answer:
2 : 3 : 4
Let seats be 50, 70, 80. New seats for Math = 50 * 1.40 = 70. New Physics = 70 * 1.50 = 105. New Biology = 80 * 1.75 = 140. New ratio = 70 : 105 : 140. Dividing by 35 gives 2 : 3 : 4.