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
611
15 men working 8 hours a day can complete a task in 20 days. How many hours a day must 20 men work to complete the same task in 12 days?
Answer:
10 hours
Step 1: M1 * H1 * D1 = M2 * H2 * D2. Step 2: 15 * 8 * 20 = 20 * H2 * 12. Step 3: 2400 = 240 * H2. H2 = 2400 / 240 = 10 hours.
612
If 24 men working 8 hours a day can finish a work in 15 days, in how many days can 20 men working 9 hours a day finish it?
Answer:
16 days
Step 1: Use the formula M1 * H1 * D1 = M2 * H2 * D2. Step 2: Substitute the values: 24 * 8 * 15 = 20 * 9 * D2. Step 3: Solve for D2: 2880 = 180 * D2. D2 = 2880 / 180 = 16 days.
613
12 men can do a piece of work in 20 days. How many days will it take for 15 men to do the same work?
Answer:
16 days
Step 1: M1 * D1 = M2 * D2. Step 2: 12 * 20 = 15 * D2. Step 3: D2 = 240 / 15 = 16 days.
614
If 40 men can build a wall in 15 days, how many men are required to build the same wall in 10 days?
Answer:
60
Step 1: Use the relationship M1 * D1 = M2 * D2. Step 2: Substitute the values: 40 * 15 = M2 * 10. Step 3: Solve for M2: M2 = (40 * 15) / 10 = 600 / 10 = 60 men.
615
36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work?
Answer:
24 days
Step 1: Use the formula M1 * D1 = M2 * D2. Step 2: Substitute the known values: 36 * 18 = 27 * D2. Step 3: Solve for D2: D2 = (36 * 18) / 27 = 648 / 27 = 24 days.
616
6 men and 8 boys can do a piece of work in 10 days, while 26 men and 48 boys can do it in 2 days. How long will 15 men and 20 boys take to do it?
Answer:
4 days
Step 1: 10(6M + 8B) = 2(26M + 48B). 60M + 80B = 52M + 96B, giving 8M = 16B or 1M = 2B. Step 2: First group in boys: 6(2B) + 8B = 20B. 20B take 10 days, so total work is 200 B-days. Step 3: Target group: 15M + 20B = 15(2B) + 20B = 50B. Time = 200 / 50 = 4 days.
617
4 men and 6 women finish a job in 8 days. 3 men and 7 women finish it in 10 days. How many days will 10 women take?
Answer:
40 days
Step 1: 8(4M + 6W) = 10(3M + 7W). 32M + 48W = 30M + 70W, giving 2M = 22W or 1M = 11W. Step 2: Total work in terms of women: 4(11W) + 6W = 50W. 50W finish in 8 days. Step 3: So 1W takes 400 days. 10 women will take 400 / 10 = 40 days.
618
2 men and 3 women can do a work in 10 days, while 3 men and 2 women can do it in 8 days. How long will 2 men and 1 woman take to do the work?
Answer:
12.5 days
Step 1: 10(2M + 3W) = 8(3M + 2W). 20M + 30W = 24M + 16W, giving 4M = 14W or 2M = 7W. Step 2: Substitute back into first scenario: 7W + 3W = 10W take 10 days. So 1W takes 100 days. Step 3: Target group: 2M + 1W = 7W + 1W = 8W. Time = 100 / 8 = 12.5 days.
619
8 men can complete a work in 20 days, and 8 women can complete the same work in 32 days. How many days will 5 men and 8 women take working together?
Answer:
16 days
Step 1: 1 man takes 8 * 20 = 160 days. 1 woman takes 8 * 32 = 256 days. Step 2: The combined rate of 5 men and 8 women is 5/160 + 8/256. Step 3: This simplifies to 1/32 + 1/32 = 2/32 = 1/16. The work will be completed in 16 days.
620
If 10 men can do a work in 15 days and 15 women can do it in 12 days, how long will 10 men and 15 women together take to do the work?
Answer:
6.67 days
Step 1: Treat '10 men' as Entity A that takes 15 days. Treat '15 women' as Entity B that takes 12 days. Step 2: We need the time for A and B together. Step 3: Rate = 1/15 + 1/12 = 4/60 + 5/60 = 9/60 = 3/20. Time = 20/3 days = 6.67 days.