# Distance and Time Quiz Set 008

### Question 1

A city bus has an average speed of 23 km/h if it doesn't stop anywhere. But if it stops in-between the average speed drops to 17 km/h. How many minutes does it stop in 1 hour?

A

\$15{15/23}\$ mins.

B

\$17{9/22}\$ mins.

C

\$13{12/25}\$ mins.

D

\$17{4/25}\$ mins.

Soln.
Ans: a

Due to stoppages, it covers a less distance of 23 - 17 = 6 in one hour. The time taken for that distance would be the wastage due to stopping = \$6/23\$ × 60 = \$15{15/23}\$ mins.

### Question 2

An aircraft was on a 1050 km journey. Its engine developed a snag so it had to slow down. It's average speed reduced by 5km/h, as a result of which it reached its destination late by 1 hour. What was the actual duration of the journey?

A

14 hrs.

B

15 hrs.

C

13 hrs.

D

16 hrs.

Soln.
Ans: a

Let x be the actual duration of the journey. Then, \$1050/x - 1050/{x + 1} = 5\$. Which gives 1050 × \$1/{x (x + 1)} = 5\$. Solving for x, or by trying the options one by one, we get x = 14 hours.

### Question 3

A cyclist travels at a speed of 8km/h. Had he travelled at 10km/h he would have covered a distance of 6 km more. What is the total distance travelled by him?

A

24 km.

B

25 km.

C

23 km.

D

26 km.

Soln.
Ans: a

By the given problem, the time is same for both cases. If the total distance covered by him at 8km/h is x, then, \$x/8 = {x + 6}/10\$. Solving, we obtain x = 24 km.

### Question 4

Bus X travels 50% faster than bus Y. They start together and meet at the same time after travelling a distance of 30km. What is the speed of the bus X, if the bus Y wasted 5 hours during its journey?

A

2 kmph.

B

3 kmph.

C

5 kmph.

D

4 kmph.

Soln.
Ans: a

Let the speed of bus X be x, and of Y be 3x/2. The difference in the times taken by them is \$30/x - 30/({3x}/2)\$ = 5, which becomes 30 × \$1/{3x}\$ = 5. Solving, we get x = 2 km/h.

### Question 5

Two trains start simultaneously. The first train moves from A to B, whereas the second train moves from B to A. After they meet at a point in between, they respectively take 144 hours and 49 hours to reach their destinations. What is the ratio of their speeds?

A

\${7/12}\$.

B

\${19/11}\$.

C

\${31/14}\$.

D

\${43/14}\$.

Soln.
Ans: a

If they take \$t_1 and t_2\$ hours respectively to reach their destinations, then the ratio of their speeds is \$√t_2 : √t_1\$. So we get \$√49 : √144\$, which gives 7 : 12, or \${7/12}\$. 