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
7221
The ratio of the number of men and women in a factory is 3:1. If there are 150 men, the total number of workers is:
Answer:
200
Men = 3x = 150 => x = 50. Total workers = 3x + 1x = 4x = 4 * 50 = 200.
7222
What least number must be added to each of the numbers 7, 16, 43, 79 so that they become proportional?
Answer:
5
Let x be added. (7+x)/(16+x) = (43+x)/(79+x). (7+x)(79+x) = (16+x)(43+x) => 553 + 86x + x^2 = 688 + 59x + x^2. 86x - 59x = 688 - 553 => 27x = 135 => x = 5.
7223
An amount is divided among P, Q, and R in ratio 2:5:7. If P and R together get Rs. 800 more than Q, then what is P's share?
Answer:
Rs. 400
Ratio is 2x, 5x, 7x. P+R = 9x. (P+R) - Q = 9x - 5x = 4x. Given 4x = 800 => x = 200. P's share = 2x = 2 * 200 = Rs. 400.
7224
The sum of three numbers is 98. If the ratio of the first to the second is 2:3 and that of the second to the third is 5:8, then the second number is:
Answer:
30
A:B = 2:3 = 10:15. B:C = 5:8 = 15:24. A:B:C = 10:15:24. Sum of parts = 49. Value of 1 part = 98 / 49 = 2. Second number (B) = 15 * 2 = 30.
7225
If x:y = 1:3, then (7x^2 + 3xy) : (2xy + y^2) is:
Answer:
16:15
Substitute x=1, y=3: Numerator = 7(1)^2 + 3(1)(3) = 7 + 9 = 16. Denominator = 2(1)(3) + 3^2 = 6 + 9 = 15. Ratio = 16:15.
7226
The prices of a scooter and a TV are in the ratio 7:5. If the scooter costs Rs. 8000 more than a TV set, then the price of the TV set is:
Answer:
Rs. 20000
Let prices be 7x and 5x. Difference = 2x = 8000 => x = 4000. Price of TV is 5x = 5 * 4000 = Rs. 20000.
7227
Two natural numbers are in the ratio 3:5 and their product is 2160. The smaller of the numbers is:
Answer:
36
Let numbers be 3x and 5x. Their product is 15x^2 = 2160. x^2 = 144 => x = 12. Smaller number is 3x = 36.
7228
A recipe calls for 2 cups of sugar for every 5 cups of flour. If 15 cups of flour are used, how many cups of sugar are needed?
Answer:
6
Ratio of sugar to flour is 2/5. Let x be sugar for 15 cups of flour. 2/5 = x/15. x = (2 * 15) / 5 = 6 cups.
7229
Find the ratio of 3 km to 300 m.
Answer:
10 : 1
Convert to same units: 3 km = 3000 m. Ratio = 3000 : 300 = 10 : 1.
7230
The ratio of two numbers is 5:6 and their LCM is 480. Find their HCF.
Answer:
16
Let numbers be 5x and 6x. Their HCF is x. LCM is 5 * 6 * x = 30x. 30x = 480 => x = 16. Therefore, their HCF is 16.