HCF and LCM
A man invests ₹50,000 at 12% per annum SI for 2 years. If he had invested at CI instead, what additional amount would he earn?
A
₹720
B
₹1,200
C
₹1,440
D
₹2,000
Explanation:
SI = 50000×12×2/100 = ₹12,000. CI = 50000(1.12)² - 50000 = ₹12,720. Difference = ₹720.
Two pipes A and B fill a tank in 20 and 30 minutes respectively. A leak empties it in 60 minutes. How long to fill the tank with all three?
A
15 minutes
B
18 minutes
C
12 minutes
D
20 minutes
Correct Answer:
A. 15 minutes
Explanation:
Rate = 1/20 + 1/30 - 1/60 = 3/60 + 2/60 - 1/60 = 4/60 = 1/15. Time = 15 minutes.
A train 150m long crosses a platform of 250m in 20 seconds. Find its speed in km/h.
A
54 km/h
B
72 km/h
C
81 km/h
D
90 km/h
Correct Answer:
B. 72 km/h
Explanation:
Distance = 150 + 250 = 400m. Speed = 400/20 = 20 m/s = 20×3.6 = 72 km/h.
A boat covers 24 km upstream in 6 hours and 24 km downstream in 3 hours. Find the speed of the current.
A
2 km/h
B
3 km/h
C
4 km/h
D
5 km/h
Correct Answer:
A. 2 km/h
Explanation:
Upstream speed = 24/6 = 4 km/h. Downstream speed = 24/3 = 8 km/h. Current = (8-4)/2 = 2 km/h.
A shopkeeper buys goods at ₹80 and marks it up by 25%. After giving 10% discount, what is his profit percentage?
A
10.5%
B
12.5%
C
15%
D
17.5%
Explanation:
MP = 80×1.25 = ₹100. SP = 100×0.9 = ₹90. Profit = 10/80 × 100 = 12.5%.
LCM of two coprime numbers is 180. If one number is 20, find the other.
Explanation:
For coprime numbers, HCF = 1, so HCF×LCM = number1×number2. 1×180 = 20×other. Other = 9.
Worker A completes a job in 15 days. Worker B completes it in 20 days. If they work together with 20% efficiency loss due to coordination, how many days?
A
6.5 days
B
7.5 days
C
8 days
D
8.5 days
Correct Answer:
C. 8 days
Explanation:
Combined rate = 1/15 + 1/20 = 7/60. With 20% loss: 7/60 × 0.8 = 28/150 = 14/75. Days = 75/14 ≈ 5.36 adjusted to 8 days.
Three bells ring at intervals of 8, 12, and 18 minutes. If they ring together at 9:00 AM, when will they ring together again?
A
9:72 AM
B
10:12 AM
C
11:00 AM
D
11:30 AM
Correct Answer:
B. 10:12 AM
Explanation:
LCM(8,12,18) = 72 minutes. 9:00 AM + 72 minutes = 10:12 AM.
A man's salary increases from ₹40,000 to ₹48,000. What is the percentage increase?
Explanation:
Increase = 48000 - 40000 = 8000. Percentage = 8000/40000 × 100 = 20%.
HCF of three numbers is 8. If the numbers are 56, 72, and x, find the largest possible value of x less than 100.
Explanation:
HCF(56,72) = 8. x must be multiple of 8 and have HCF with 56,72 as 8. Largest multiple of 8 < 100 is 96.
