# Distance and Time Quiz Set 019

### Question 1

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 2

A boy goes to his school at an average speed of 3 km/h, and returns back at an average speed of 5 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 × 3 × 5}/{3 + 5}\$ = \${15/4}\$, which is same as: \$3{3/4}\$ km/h.

### Question 3

Two trains start simultaneously. The first train moves from Mumbai to Baroda, whereas the second train moves from Baroda to Mumbai. After they meet at a point in between, they respectively take 16 hours and 4 hours to reach their destinations. What is the ratio of their speeds?

A

\${1/2}\$.

B

\${3/2}\$.

C

\${5/2}\$.

D

\${7/4}\$.

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 \$√4 : √16\$, which gives 2 : 4, or \${1/2}\$.

### Question 4

Speeds of A and B are in the ratio 3 : 1. What is the speed of A if B can cover a distance of 2 Km in 1 hour?

A

6 kmph.

B

7 kmph.

C

5 kmph.

D

8 kmph.

Soln.
Ans: a

The speed of B is 2/1 = 2 km/h. So, the speed of A = \${3 × 2}/1\$ = 6 km/h.

### Question 5

A train passes two persons walking in the same direction as the train. The time it takes to move past the man running at 37km/h is 17sec, whereas the time it takes to cross the other man running at 44km/h is 18sec. What is the speed of the train?

A

163km/h.

B

164km/h.

C

162km/h.

D

165km/h.

Soln.
Ans: a

Let the speed of the train be v km/h. Length of the train calculated with the data for the first man = \$(v - 37) × 17\$. It should equal the length obtained from the data for the second man. So \$(v - 37) × 17\$ = \$(v - 44) × 18\$. Please note that we have not converted seconds to hours because that factor will ultimately cancel away. Solving for v we get 163km/h.