Numbers
Three pipes A, B, and C can fill a tank in 6, 8, and 12 hours respectively. If all three are opened together, what fraction of the tank is filled in 1 hour?
A 9/24
B 12/24
C 15/24
D 18/24
Explanation:
Combined rate = 1/6 + 1/8 + 1/12 = 4/24 + 3/24 + 2/24 = 9/24
A train 180m long crosses another train 220m long coming towards it in 9 seconds. If the first train's speed is 40 km/h, what is the speed of the second train?
A 50 km/h
B 32 km/h
C 48 km/h
D 36 km/h
Correct Answer:
B. 32 km/h Explanation:
Total distance = 180 + 220 = 400m. Relative speed = 400/9 m/s = 160 km/h. Speed of second train = 160 - 40 = 32 km/h
A man sells an item for Rs. 1200 at 20% profit. What is the cost price?
A Rs. 1000
B Rs. 900
C Rs. 1100
D Rs. 960
Correct Answer:
A. Rs. 1000 Explanation:
CP = 1200 × 100/120 = Rs. 1000
A cistern has a drain pipe that empties it in 20 hours. If an inlet pipe fills it in 15 hours, how long will it take to fill if both are open?
A 60 hours
B 45 hours
C 50 hours
D 55 hours
Correct Answer:
A. 60 hours Explanation:
Net rate = 1/15 - 1/20 = 4/60 - 3/60 = 1/60. Time = 60 hours
A merchant bought goods for Rs. 8000. He marked them 50% above cost price but gave a discount of 10%. What is his profit?
A Rs. 1200
B Rs. 1400
C Rs. 1600
D Rs. 1800
Correct Answer:
C. Rs. 1600 Explanation:
Marked Price = 8000 × 150/100 = 12000. Selling Price = 12000 × 90/100 = 10800. Profit = 10800 - 8000 = Rs. 1600
Two taps A and B can fill a tank in 20 and 30 minutes respectively. A third tap C empties it in 40 minutes. If all three are opened together, in how many minutes will the tank be full?
A 15 minutes
B 17.14 minutes
C 18 minutes
D 19 minutes
Correct Answer:
B. 17.14 minutes Explanation:
Net rate = 1/20 + 1/30 - 1/40 = 6/120 + 4/120 - 3/120 = 7/120. Time = 120/7 ≈ 17.14 minutes
A boat takes 3 hours to travel 72 km downstream and 6 hours to travel the same distance upstream. What is the speed of the current?
A 4 km/h
B 6 km/h
C 8 km/h
D 5 km/h
Correct Answer:
B. 6 km/h Explanation:
Downstream speed = 72/3 = 24 km/h. Upstream speed = 72/6 = 12 km/h. Current = (24-12)/2 = 6 km/h
A sum becomes Rs. 14400 in 2 years at 20% per annum compound interest. What is the principal?
A Rs. 10000
B Rs. 12000
C Rs. 15000
D Rs. 18000
Correct Answer:
A. Rs. 10000 Explanation:
P(1.2)² = 14400. P × 1.44 = 14400. P = Rs. 10000
X can do a work in 12 days, Y can do it in 18 days. They work together for 3 days, then X leaves. In how many more days will Y complete the work?
A 10.5 days
B 9 days
C 11 days
D 12 days
Correct Answer:
A. 10.5 days Explanation:
Work done in 3 days = 3(1/12 + 1/18) = 3(3/36 + 2/36) = 3 × 5/36 = 5/12. Remaining = 7/12. Y completes 7/12 in (7/12)/(1/18) = 7/12 × 18 = 10.5 days
If 15% of a number is 45, what is 40% of that number?
Explanation:
Number = 45 × 100/15 = 300. 40% of 300 = 300 × 40/100 = 120
