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Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).
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Question 1 of 5
1. Question
A bus for Bangalore leaves every thirty minutes. An enquiry clerk told the passenger that the bus had already left 15 minutes ago and the next bus will leave at 10:45 am. At what time did the clerk give the information to the passenger?
Correct
Answer: B
Solution:
At 10:45 am the next bus leaves it means the previous bus left at 10:15 am and the clerk
informed the passenger at 10:30 am.
Incorrect
Answer: B
Solution:
At 10:45 am the next bus leaves it means the previous bus left at 10:15 am and the clerk
informed the passenger at 10:30 am.
-
Question 2 of 5
2. Question
A boat takes 4 hours to travel 32 km downstream and 8 hours to cover the same distance upstream.
Consider the following statements:
Statement I: The speed of the boat in still water is 6 km/h.
Statement II: The speed of the current is 2 km/h.
Statement III: If the river had no current, the boat would take 5 hours 20 minutes to cover 32 km.How many of the above statements are correct?
Correct
Answer: (c)
Explanation:
Downstream = 32 ÷ 4 = 8 km/h.
Upstream = 32 ÷ 8 = 4 km/h.
Still water speed = (8 + 4)/2 = 6 km/h.
Current speed = (8 − 4)/2 = 2 km/h.
So Statements I and II are correct.
If no current, speed = 6 km/h → time = 32 ÷ 6 = 5.33 h = 5 h 20 min.
Statement III also correct.
Hence, all three correct → (c).Incorrect
Answer: (c)
Explanation:
Downstream = 32 ÷ 4 = 8 km/h.
Upstream = 32 ÷ 8 = 4 km/h.
Still water speed = (8 + 4)/2 = 6 km/h.
Current speed = (8 − 4)/2 = 2 km/h.
So Statements I and II are correct.
If no current, speed = 6 km/h → time = 32 ÷ 6 = 5.33 h = 5 h 20 min.
Statement III also correct.
Hence, all three correct → (c). -
Question 3 of 5
3. Question
Two trains start from stations A and B towards each other at the same time. After crossing each other, the trains take 9 hours and 16 hours respectively to reach their destinations. Find the ratio of their speeds.
Correct
Answer: B
Solution:
Let the speed of the trains be S₁ and S₂.
When two trains start from opposite ends and meet, the ratio of their speeds is inversely proportional to the time taken after meeting to reach their destinations.
Therefore, S₁ : S₂ = √(Time₂) : √(Time₁)
⇒ S₁ : S₂ = √16 : √9 = 4 : 3
Hence, the required ratio of their speeds is 4 : 3.
So, option (b) is the correct answer.Incorrect
Answer: B
Solution:
Let the speed of the trains be S₁ and S₂.
When two trains start from opposite ends and meet, the ratio of their speeds is inversely proportional to the time taken after meeting to reach their destinations.
Therefore, S₁ : S₂ = √(Time₂) : √(Time₁)
⇒ S₁ : S₂ = √16 : √9 = 4 : 3
Hence, the required ratio of their speeds is 4 : 3.
So, option (b) is the correct answer. -
Question 4 of 5
4. Question
Point P lies between two towns A and B such that the distance from P to B is five times the distance from A to P. A car starts from A towards B and at the same time a truck starts from B towards A. The truck reaches P 3 hours after the car had already reached P. If the speed of the truck is 50% (i.e. 1/2) of the speed of the car, then the time taken by the car to reach P from A is:
Correct
Answer: A
Solution:
Let AP = d km. Then BP = 5d km.
Let the car take “t” hours to reach P. Then speed of car = d/t km/hr.
Speed of truck = 1/2 of this = (1/2)(d/t) = d/(2t) km/hr.
Truck reaches P 3 hours later than car, so truck takes (t + 3) hours to reach P.
Distance covered by truck = BP = 5d km.
So 5d = (d/(2t)) × (t + 3)
5d = d(t + 3)/(2t)
Divide both sides by d:
5 = (t + 3)/(2t)
Cross-multiply:
5 × 2t = t + 3
10t = t + 3
10t – t = 3
9t = 3
t = 3/9 = 1/3 hour
1/3 hour = 20 minutes
So, option (a) is the correct answer.Incorrect
Answer: A
Solution:
Let AP = d km. Then BP = 5d km.
Let the car take “t” hours to reach P. Then speed of car = d/t km/hr.
Speed of truck = 1/2 of this = (1/2)(d/t) = d/(2t) km/hr.
Truck reaches P 3 hours later than car, so truck takes (t + 3) hours to reach P.
Distance covered by truck = BP = 5d km.
So 5d = (d/(2t)) × (t + 3)
5d = d(t + 3)/(2t)
Divide both sides by d:
5 = (t + 3)/(2t)
Cross-multiply:
5 × 2t = t + 3
10t = t + 3
10t – t = 3
9t = 3
t = 3/9 = 1/3 hour
1/3 hour = 20 minutes
So, option (a) is the correct answer. -
Question 5 of 5
5. Question
The following question is accompanied by three statements 1, 2, and 3. You have to determine which statement(s) is/are necessary to answer the question.
A man rows a boat from village A to village B and back. What is his speed in still water?
- The time taken to go from A to B downstream is 2 hours.
- The time taken to come back from B to A upstream is 3 hours.
- The speed of the stream is 2 km/hr.
Select the correct answer using the codes given below.
Correct
Answer: D
Solution:
Let the distance between A and B be D km, speed in still water be B km/hr, and speed of stream be S km/hr.
From statement 1: D/(B + S) = 2 → D = 2(B + S)
From statement 2: D/(B – S) = 3 → D = 3(B – S)
Equate D from both:
2(B + S) = 3(B – S)
2B + 2S = 3B – 3S
2S + 3S = 3B – 2B
5S = B
So we get B in terms of S, but not the numerical value of B.
From statement 3: S = 2 km/hr
So B = 5S = 5 × 2 = 10 km/hr
Thus, to get an actual numerical value of speed in still water, we need all three statements.
Hence, option (d) is the correct answer.Incorrect
Answer: D
Solution:
Let the distance between A and B be D km, speed in still water be B km/hr, and speed of stream be S km/hr.
From statement 1: D/(B + S) = 2 → D = 2(B + S)
From statement 2: D/(B – S) = 3 → D = 3(B – S)
Equate D from both:
2(B + S) = 3(B – S)
2B + 2S = 3B – 3S
2S + 3S = 3B – 2B
5S = B
So we get B in terms of S, but not the numerical value of B.
From statement 3: S = 2 km/hr
So B = 5S = 5 × 2 = 10 km/hr
Thus, to get an actual numerical value of speed in still water, we need all three statements.
Hence, option (d) is the correct answer.
