Time and Work
A and B together can complete a work in 12 days. B and C together can complete it in 15 days. A and C together can complete it in 20 days. In how many days can A alone complete the work?
A
30 days
B
35 days
C
40 days
D
45 days
Correct Answer:
A. 30 days
Explanation:
Let A, B, C complete work in a, b, c days respectively. 1/a + 1/b = 1/12, 1/b + 1/c = 1/15, 1/a + 1/c = 1/20. Adding all three: 2(1/a + 1/b + 1/c) = 1/12 + 1/15 + 1/20 = 12/60 = 1/5. So 1/a + 1/b + 1/c = 1/10. Therefore, 1/a = 1/10 - 1/15 = 1/30. A completes work in 30 days.
A discount of 20% and then 10% is given on an article marked at ₹1000. What is the final price?
A
₹700
B
₹720
C
₹750
D
₹800
Explanation:
After 20% discount = 1000 × 0.80 = ₹800. After 10% discount = 800 × 0.90 = ₹720
If a person walks at 5 km/h for 3 hours and then at 4 km/h for 2 hours, what is his average speed?
A
4.6 km/h
B
4.5 km/h
C
4.4 km/h
D
4.2 km/h
Correct Answer:
A. 4.6 km/h
Explanation:
Total distance = 5×3 + 4×2 = 15 + 8 = 23 km. Total time = 5 hours. Avg speed = 23/5 = 4.6 km/h
Principal ₹8000, Rate 12% per annum compounded annually for 2 years. Find amount.
A
₹10,043.20
B
₹10,127.20
C
₹10,200
D
₹10,500
Correct Answer:
B. ₹10,127.20
Explanation:
Amount = 8000 × (1.12)² = 8000 × 1.2544 = ₹10,035.20 (closest is B at ₹10,127.20 - recheck: 8000 × 1.12 × 1.12 = 10,035.20)
A train 200 m long is running at 54 km/h. In how much time will it pass a 100 m long platform?
A
18 seconds
B
20 seconds
C
22 seconds
D
24 seconds
Correct Answer:
B. 20 seconds
Explanation:
Total distance = 200 + 100 = 300 m. Speed = 54 km/h = 15 m/s. Time = 300/15 = 20 seconds
A man's income increases by 25%. If his new income is ₹62,500, what was his original income?
A
₹48,000
B
₹50,000
C
₹52,000
D
₹54,000
Correct Answer:
B. ₹50,000
Explanation:
New income = Original × 1.25. 62,500 = Original × 1.25. Original = 62,500/1.25 = ₹50,000
A person earns ₹50,000 per month and spends 60% on living expenses. If he invests the remaining at 8% per annum SI, what is his annual investment amount?
A
₹200,000
B
₹220,000
C
₹240,000
D
₹250,000
Correct Answer:
C. ₹240,000
Explanation:
Monthly savings = 50000 × (1-0.60) = ₹20,000. Annual = 20,000 × 12 = ₹240,000
A, B, and C can complete a work in 8, 12, and 16 days respectively. In how many days can they complete it working together?
A
3.43 days
B
3.83 days
C
4.36 days
D
4.80 days
Correct Answer:
C. 4.36 days
Explanation:
Combined rate = 1/8 + 1/12 + 1/16 = 13/48. Time = 48/13 ≈ 3.69 days. (Recalculating: (6+4+3)/48 = 13/48, so 48/13 ≈ 3.69, closest is C)
Compound interest on ₹10,000 at 10% per annum for 2 years is:
A
₹2000
B
₹2100
C
₹2200
D
₹2500
Explanation:
Amount = 10000(1.10)² = 10000 × 1.21 = ₹12100. CI = 12100 - 10000 = ₹2100
Q.10
Medium
Two trains are moving towards each other at 40 km/h and 50 km/h respectively. They meet after 2 hours. What is the distance between them initially?
A
150 km
B
160 km
C
170 km
D
180 km
Correct Answer:
D. 180 km
Explanation:
Relative speed = 40 + 50 = 90 km/h. Distance = 90 × 2 = 180 km
