# Distance and Time Quiz Set 009

### Question 1

An aircraft was on a 2660 km journey. Its engine developed a snag so it had to slow down. It's average speed reduced by 7km/h, as a result of which it reached its destination late by 1 hour. What was the actual duration of the journey?

A

19 hrs.

B

20 hrs.

C

18 hrs.

D

21 hrs.

Soln.
Ans: a

Let x be the actual duration of the journey. Then, \$2660/x - 2660/{x + 1} = 7\$. Which gives 2660 × \$1/{x (x + 1)} = 7\$. Solving for x, or by trying the options one by one, we get x = 19 hours.

### Question 2

A boy goes to his school at an average speed of 5 km/h, and returns back at an average speed of 3 km/h. What is the average speed for the to and fro journey?

A

\$3{3/4}\$ km/h.

B

\$6{1/3}\$ km/h.

C

\$1{5/6}\$ km/h.

D

\$4{1/2}\$ km/h.

Soln.
Ans: a

If u and v are the to and fro speeds, then the standard formula is \${2uv}/{u + v}\$ = \${2 × 5 × 3}/{5 + 3}\$ = \${15/4}\$, which is same as: \$3{3/4}\$ km/h.

### Question 3

A vehicle travels 50% of its distance at 4 km/h, and the remaining 50% at 8 km/h. What is the total distance, if it travelled for a total duration of 24 hours?

A

128 km.

B

129 km.

C

127 km.

D

130 km.

Soln.
Ans: a

Let 2x be the actual duration of the journey. Then, \$x/4 + x/8 = 24\$. Solving for x we get x = 64, and so, 2x = 128 km.

### Question 4

Speeds of A and B are in the ratio 7 : 19. What is the ratio of the times that they will take to cover a distance of 100 km?

A

19 : 7.

B

7 : 19.

C

19 : 100.

D

100 : 7.

Soln.
Ans: a

Let the speeds be 7x and 19x. The times they take to cover 100 km are \$100/{7x}\$ and \$100/{19x}\$. The ratio would be 19 : 7.

### Question 5

Bus X travels 50% faster than bus Y. They start together and meet at the same time after travelling a distance of 72km. What is the speed of the bus X, if the bus Y wasted 6 hours during its journey?

A

4 kmph.

B

5 kmph.

C

3 kmph.

D

6 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 \$72/x - 72/({3x}/2)\$ = 6, which becomes 72 × \$1/{3x}\$ = 6. Solving, we get x = 4 km/h. 