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
8 men can do a piece of work in 20 days, and 8 women can do the same work in 32 days. In how many days can 5 men and 8 women do it?
Answer:
16 days
1M takes 8*20 = 160 days. 1W takes 8*32 = 256 days. (5M + 8W)'s 1 day work = 5/160 + 8/256 = 1/32 + 1/32 = 2/32 = 1/16. Time = 16 days.
162
12 men can complete a work in 15 days, and 20 women can complete the same work in 12 days. How many days will 5 men and 5 women take to complete the work?
Answer:
20 4/7 days
1M takes 12*15 = 180 days. 1W takes 20*12 = 240 days. (5M + 5W)'s 1 day work = 5/180 + 5/240 = 1/36 + 1/48 = (4+3)/144 = 7/144. Time = 144/7 = 20 4/7 days.
163
3 men or 5 women can do a piece of work in 43 days. How long will 5 men and 6 women take to finish it?
Answer:
15 days
3M = 5W. Work = 3M * 43. 5M + 6W = 5M + 6*(3/5)M = 5M + 3.6M = 8.6M. Time = (3 * 43) / 8.6 = 129 / 8.6 = 15 days.
164
10 men or 20 boys can do a work in 20 days. How many days will 5 men and 10 boys take to do it?
Answer:
20 days
10M = 20B => 1M = 2B. 5M + 10B = 5M + 5M = 10M. Since 10M take 20 days, the group will take 20 days.
165
4 men or 6 women can finish a piece of work in 12 days. In how many days can 2 men and 3 women finish it?
Answer:
12 days
4M = 6W. 2M + 3W = 2M + 2M = 4M. Since 4M can finish it in 12 days, the combined group of 2M and 3W will also finish it in exactly 12 days.
166
2 men or 3 women can do a piece of work in 96 days. In how many days can 6 men and 7 women do the same work?
Answer:
18 days
2M = 3W => M = 1.5W. 3W take 96 days, so 1W takes 288 days. We need (6M + 7W) = 6(1.5W) + 7W = 9W + 7W = 16W. 16W will take 288 / 16 = 18 days.
167
A is 60% more efficient than B. If B alone can complete a work in 40 days, in how many days can they complete it together?
Answer:
15.38 days
B's rate = 1/40. A's rate = 1.6 * (1/40) = 1/25. Combined rate = 1/40 + 1/25 = (5+8)/200 = 13/200. Time = 200/13 = 15.38 days.
168
The ratio of efficiencies of A and B is 3:4. If they work together, they can complete a job in 12 days. In how many days can A alone complete it?
Answer:
28 days
Efficiencies are 3x and 4x. Total efficiency = 7x. Total work = 7x * 12 = 84x. A's time = Total Work / A's efficiency = 84x / 3x = 28 days.
169
A takes 40 days less than B to complete a work because A is twice as fast as B. How many days will A take to complete it alone?
Answer:
40 days
Let A take x days, B takes 2x days. Difference = x = 40. Therefore, A takes 40 days.
170
A is thrice as good a workman as B and therefore is able to finish a job in 60 days less than B. Working together, they can do it in:
Answer:
22.5 days
Let A take x days, B takes 3x days. Difference = 2x = 60 => x = 30. A takes 30 days, B takes 90 days. Together: (30*90)/(30+90) = 2700/120 = 22.5 days.