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
61
A, B, and C get a contract for $550. A and B together do 7/11 of the work. How much does C get?
Answer:
$200
Step 1: Since A and B do 7/11 of the work, C must do the remaining part. Step 2: C's share of the work is 1 - 7/11 = 4/11. Step 3: C's payment = (4/11) * $550 = $200.
62
A and B take a job for $450. A can do it in 10 days, B in 15 days. With C's assistance, they complete it in 5 days. Find C's share.
Answer:
$75
Step 1: Work done by A in 5 days = 5/10 = 1/2. Work done by B in 5 days = 5/15 = 1/3. Step 2: Work done by C = 1 - (1/2 + 1/3) = 1/6. Step 3: C's share = 1/6 of $450 = $75.
63
A and B undertake a contract for $300. A can do it alone in 8 days, and B in 12 days. With C's help, they finish it in 4 days. What is C's share?
Answer:
$50
Step 1: In 4 days, A does 4/8 = 1/2 of the work. B does 4/12 = 1/3 of the work. Step 2: C does the remaining work: 1 - (1/2 + 1/3) = 1 - 5/6 = 1/6. Step 3: Since wages are distributed based on work done, C's share is 1/6 of $300 = $50.
64
A, B, and C can complete a task in 10, 15, and 18 days respectively. They get $150 for the job. What is A's share?
Answer:
$67.5
Step 1: The ratio of their efficiencies is (1/10) : (1/15) : (1/18). Multiplying by LCM 90 gives 9:6:5. Step 2: Total parts = 9 + 6 + 5 = 20. Step 3: A's share = (9/20) * $150 = $67.5.
65
A, B, and C can do a work in 6, 8, and 12 days respectively. Together they earn $135. What is B's share?
Answer:
$45
Step 1: Efficiency ratio A:B:C = (1/6) : (1/8) : (1/12) = 4:3:2. Step 2: Total parts = 4 + 3 + 2 = 9. B's share is 3 parts. Step 3: B's share = (3/9) * $135 = $45.
66
X and Y can do a job in 20 and 30 days respectively. They complete it together and earn $100. How much does X receive?
Answer:
$60
Step 1: The ratio of efficiencies of X:Y is (1/20) : (1/30) = 3:2. Step 2: Total parts = 5. X's share corresponds to 3 parts. Step 3: X's share = (3/5) * $100 = $60.
67
A and B can complete a work in 12 and 24 days respectively. They undertake a job for $60. Find B's share.
Answer:
$20
Step 1: Efficiency ratio of A:B = (1/12) : (1/24) = 2:1. Step 2: Total parts = 3. B's share is 1 part. Step 3: B's share = (1/3) * $60 = $20.
68
A and B can do a piece of work in 10 and 15 days respectively. They work together and earn $50. What is A's share?
Answer:
$30
Step 1: Wages are divided in the ratio of efficiencies. A's eff : B's eff = (1/10) : (1/15) = 3:2. Step 2: Total parts = 5. A's share is 3 parts. Step 3: A's share = (3/5) * $50 = $30.
69
A garrison of 120 men has provisions for 200 days. After 5 days, 30 men die due to an epidemic. How long will the remaining food last?
Answer:
260 days
Step 1: After 5 days, the remaining food is enough for 120 men for 195 days. This equals 120 * 195 = 23400 man-days of food. Step 2: The remaining number of men is 120 - 30 = 90 men. Step 3: Time the food lasts = 23400 / 90 = 260 days.
70
30 men can do a work in 16 days. After 6 days, 10 men leave. In how many days will the remaining work be finished?
Answer:
15 days
Step 1: Total work = 30 * 16 = 480 man-days. Work done in 6 days = 30 * 6 = 180 man-days. Step 2: Remaining work = 480 - 180 = 300 man-days. Step 3: Remaining men = 30 - 10 = 20. Time to finish = 300 / 20 = 15 days.