Q.31
Medium
The speed of a boat in still water is 12 km/h. If the speed of the current is 3 km/h, what is the speed downstream?
A
14 km/h
B
15 km/h
C
16 km/h
D
18 km/h
Correct Answer:
B. 15 km/h
Explanation:
Speed downstream = Speed in still water + Speed of current = 12 + 3 = 15 km/h
Q.32
Medium
If (x + 2)² = 36, what is the value of x?
A
4 or -8
B
4 or 6
C
6 or -6
D
-4 or 8
Correct Answer:
A. 4 or -8
Explanation:
Taking square root: x + 2 = ±6. So x = 4 or x = -8
Q.33
Medium
A rectangular field has length 80 m and breadth 60 m. What is the cost of fencing it at Rs. 25 per meter?
A
Rs. 6,500
B
Rs. 7,000
C
Rs. 7,500
D
Rs. 8,000
Correct Answer:
B. Rs. 7,000
Explanation:
Perimeter = 2(80 + 60) = 280 m. Cost = 280 × 25 = Rs. 7,000
Q.34
Medium
The average age of 8 people is 35 years. If one person of age 45 leaves the group, what is the new average age?
A
32.14 years
B
33.57 years
C
34.2 years
D
35.5 years
Correct Answer:
B. 33.57 years
Explanation:
Total age of 8 people = 8 × 35 = 280 years. After removal: total = 280 - 45 = 235. New average = 235/7 = 33.57 years
Q.35
Medium
If x³ = 729, what is the value of x?
Explanation:
x = ∛729 = 9 (since 9 × 9 × 9 = 729)
Q.36
Medium
Two pipes A and B can fill a tank in 20 hours and 30 hours respectively. If both pipes are opened together with pipe C which empties the tank in 60 hours, how long will it take to fill the tank?
A
12 hours
B
15 hours
C
18 hours
D
20 hours
Correct Answer:
B. 15 hours
Explanation:
Rate of A = 1/20, Rate of B = 1/30, Rate of C = -1/60. Combined rate = 1/20 + 1/30 - 1/60 = 3/60 + 2/60 - 1/60 = 4/60 = 1/15. Time = 15 hours.
Q.37
Medium
If the length of a rectangle is increased by 20% and breadth is decreased by 10%, what is the percentage change in area?
A
8% increase
B
10% increase
C
8% decrease
D
12% increase
Correct Answer:
A. 8% increase
Explanation:
Original area = L × B. New area = 1.2L × 0.9B = 1.08LB. Change = 1.08LB - LB = 0.08LB = 8% increase.
Q.38
Medium
A train travels 360 km in 6 hours. What is its average speed in m/s?
A
12.5 m/s
B
16.67 m/s
C
20 m/s
D
25 m/s
Correct Answer:
B. 16.67 m/s
Explanation:
Speed = 360/6 = 60 km/h. Convert to m/s: 60 × (5/18) = 300/18 = 16.67 m/s.
Q.39
Medium
The difference between compound interest and simple interest on Rs. 5000 for 2 years at 10% per annum is:
A
Rs. 25
B
Rs. 50
C
Rs. 75
D
Rs. 100
Correct Answer:
B. Rs. 50
Explanation:
SI = (5000 × 10 × 2)/100 = 1000. CI = 5000(1.1)² - 5000 = 5000(1.21 - 1) = 1050. Difference = 1050 - 1000 = 50.
Q.40
Medium
If a:b = 3:4 and b:c = 5:6, what is a:c?
A
3:8
B
15:24
C
5:8
D
9:16
Explanation:
a:b = 3:4 means a/b = 3/4. b:c = 5:6 means b/c = 5/6. a/c = (a/b) × (b/c) = (3/4) × (5/6) = 15/24. So a:c = 15:24.
