Explore topic-wise InterviewSolutions in .

This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.

51.	In covering a certain distance, the speeds of A and B are in the ratio 3 : 4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is (a) 1 hour (b) \(1\frac12\) hours (c) 2 hours (d) \(2\frac12\) hours
Answer» (c) 2 hrs Ratio of speeds = 3 : 4 ⇒ Ratio of times taken = 4 : 3 Let A and B take 4x and 3x hrs to reach the destination. Then, 4x – 3x = \(\frac{30}{60}=\frac12\) ⇒ \(x=\frac12\) Time taken by A = \(\bigg(4\times\frac12\bigg)\) hrs = 2 hrs.

51.

In covering a certain distance, the speeds of A and B are in the ratio 3 : 4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is (a) 1 hour (b) \(1\frac12\) hours (c) 2 hours (d) \(2\frac12\) hours

Answer»

(c) 2 hrs

Ratio of speeds = 3 : 4

⇒ Ratio of times taken = 4 : 3

Let A and B take 4x and 3x hrs to reach the destination. Then, 4x – 3x = \(\frac{30}{60}=\frac12\) ⇒ \(x=\frac12\)

Time taken by A = \(\bigg(4\times\frac12\bigg)\) hrs = 2 hrs.

Discussion

52.	The ratio between the rates of walking of A and B is 2 : 3 and therefore A takes 10 minutes more than the time taken by B to reach the destination. If A had walked at double the speed, then in what time would he have covered that distance?
Answer» Ratio of speeds = 2 : 3 ⇒ Ratio of times taken = 3 : 2 Given 3x – 2x = 10 ⇒ x = 10 ⇒A would have taken 30 minutes. But if A walks with double the speed, then he takes half the time, i.e., 15 minutes.

52.

The ratio between the rates of walking of A and B is 2 : 3 and therefore A takes 10 minutes more than the time taken by B to reach the destination. If A had walked at double the speed, then in what time would he have covered that distance?

Answer»

Ratio of speeds = 2 : 3

⇒ Ratio of times taken = 3 : 2

Given 3x – 2x = 10 ⇒ x = 10

⇒A would have taken 30 minutes. But if A walks with double the speed, then he takes half the time, i.e., 15 minutes.

Discussion

53.	A train X starts from New Delhi at 4 pm and reaches Ghaziabad at 5 pm. While another train Y starts from Ghaziabad at 4 pm and reaches New Delhi at 5 : 30 pm. At what time will the two trains cross each other?
Answer» Let Delhi – Ghaziabad distance be a km. Then, Speed of train X = a km/hr Speed of train Y = \(\frac{a}{\frac{3}{2}}\) km/hr = \(\frac{2a}{3}\) km/hr Suppose they meet after b hours, then \(ab + \frac{2ab}{3} =a ⇒\frac{5b}{3}=1⇒b=\frac35\) hrs = 36 minutes ∴ They meet at 4 : 36 pm.

53.

A train X starts from New Delhi at 4 pm and reaches Ghaziabad at 5 pm. While another train Y starts from Ghaziabad at 4 pm and reaches New Delhi at 5 : 30 pm. At what time will the two trains cross each other?

Answer»

Let Delhi – Ghaziabad distance be a km. Then,

Speed of train X = a km/hr

Speed of train Y = \(\frac{a}{\frac{3}{2}}\) km/hr = \(\frac{2a}{3}\) km/hr

Suppose they meet after b hours, then \(ab + \frac{2ab}{3} =a ⇒\frac{5b}{3}=1⇒b=\frac35\) hrs = 36 minutes

∴ They meet at 4 : 36 pm.

Discussion

54.	A train increases its normal speed by 12.5% and reaches its destination 20 minutes earlier. What is the actual time taken by the train in the journey? (a) 220 min (b) 180 min (c) 145 min (d) 160 min
Answer» (b) 180 min Let the normal speed of the train be x metres/ minute and the actual time taken by the train in the journey be t minutes. Then, \(x\times{t} = \frac{112.5x}{100}\times(t-20)\) ⇒ \(t = \frac{112.5t}{100}-22.5 ⇒\frac{112.5t}{100}-t=22.5\) ⇒ \(\frac{12.5t}{100}=22.5 ⇒ t = \frac{22.5\times100}{12.5}\) minutes = 180 min.

54.

A train increases its normal speed by 12.5% and reaches its destination 20 minutes earlier. What is the actual time taken by the train in the journey? (a) 220 min (b) 180 min (c) 145 min (d) 160 min

Answer»

(b) 180 min

Let the normal speed of the train be x metres/ minute and the actual time taken by the train in the journey be t minutes. Then,

\(x\times{t} = \frac{112.5x}{100}\times(t-20)\)

⇒ \(t = \frac{112.5t}{100}-22.5 ⇒\frac{112.5t}{100}-t=22.5\)

⇒ \(\frac{12.5t}{100}=22.5 ⇒ t = \frac{22.5\times100}{12.5}\) minutes = 180 min.

Discussion