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
Divide 50 into two parts so that the sum of their reciprocals is 1/12. What are the two parts?
Answer:
20, 30
Let parts be x and 50-x. 1/x + 1/(50-x) = 1/12. (50-x+x) / (x(50-x)) = 1/12 => 50 / (50x - x^2) = 1/12 => 600 = 50x - x^2. Solving x^2 - 50x + 600 = 0 gives (x-20)(x-30) = 0. Parts are 20 and 30.
162
The ratio of the angles of a triangle is 2:3:4. What is the measure of the smallest angle?
Answer:
40 degrees
Sum of angles of a triangle is 180. Total parts = 2+3+4 = 9. 1 part = 180/9 = 20. Smallest angle = 2 parts = 2 * 20 = 40 degrees.
163
The ratio of copper and zinc in brass is 13:7. How much zinc will be there in 100 kg of brass?
Answer:
35 kg
Total parts = 13 + 7 = 20. Zinc share = (7/20) * 100 = 35 kg.
164
If x : y = 3 : 2, then the ratio 2x^2 + 3y^2 : 3x^2 - 2y^2 is equal to:
Answer:
30 : 19
Substitute x=3, y=2: Numerator = 2(9) + 3(4) = 18 + 12 = 30. Denominator = 3(9) - 2(4) = 27 - 8 = 19. Ratio is 30 : 19.
165
Two numbers are in the ratio 1:3. If their sum is 240, then their difference is:
Answer:
120
Let numbers be x and 3x. Sum = 4x = 240 => x = 60. Difference = 3x - x = 2x = 2 * 60 = 120.
166
The ratio of the number of boys to girls in a school of 720 students is 7:5. How many more girls should be admitted to make the ratio 1:1?
Answer:
120
Total parts = 12. 1 part = 720/12 = 60. Boys = 7*60=420. Girls = 5*60=300. To make ratio 1:1, girls must be equal to boys (420). Girls to be added = 420 - 300 = 120.
167
If an amount of Rs. 990 is divided among A, B, and C in the ratio 3:4:2, then B will get:
Answer:
Rs. 440
Total parts = 3+4+2 = 9. B's share = (4/9) * 990 = 4 * 110 = Rs. 440.
168
If 40% of a number is equal to two-third of another number, what is the ratio of first number to the second number?
Answer:
5:3
0.4A = (2/3)B => (2/5)A = (2/3)B => A/B = (2/3) * (5/2) = 5/3. Ratio is 5:3.
169
The ratio of the cost price and selling price is 4:5. The profit percent is:
Answer:
25%
CP = 4x, SP = 5x. Profit = x. Profit % = (Profit/CP)*100 = (x/4x)*100 = 25%.
170
Two numbers are in the ratio 3:5. If 9 is subtracted from each, the new numbers are in the ratio 12:23. The smaller number is:
Answer:
33
Let numbers be 3x, 5x. (3x-9)/(5x-9) = 12/23. 69x - 207 = 60x - 108 => 9x = 99 => x = 11. Smaller number = 33.