# Distance and Time Quiz Set 012

### Question 1

Two cars, A and B, start to move towards each other. If they meet when A has travelled \$(1/5)\$th of the distance, what is the ratio of the speed of B to the speed of A?

A

4.

B

5.

C

3.

D

6.

Soln.
Ans: a

Let the speeds of the cars be u and v and the initial distance between them be L. When they meet they have travelled for the same time. So \$(L/5)/u = ({4L}/5)/v\$. The ratio \$v/u\$ = 4.

### Question 2

Two cars A and B begin to move towards each other and meet midway after travelling equal distance. What is the initial distance between them if the speeds of A and B are 2 km/h and 8 km/h, and B started 1 hour late?

A

\$5{1/3}\$ km.

B

\$9{1/2}\$ km.

C

\$4{1/3}\$ km.

D

5 km.

Soln.
Ans: a

If the distance between them is L, they meet after travelling L/2. Equating the times they travelled, \$L/{2 × 2} = L/{2 × 8} + 1\$. Solving for L we get L = \$5{1/3}\$ km.

### Question 3

A vehicle travels 50% of its distance at 5 km/h, and the remaining 50% at 11 km/h. What is the total distance, if it travelled for a total duration of 32 hours?

A

220 km.

B

221 km.

C

219 km.

D

222 km.

Soln.
Ans: a

Let 2x be the actual duration of the journey. Then, \$x/5 + x/11 = 32\$. Solving for x we get x = 110, and so, 2x = 220 km.

### Question 4

Speeds of A and B are in the ratio 17 : 11. What is the speed of A if B can cover a distance of 55 Km in 1 hour?

A

85 kmph.

B

86 kmph.

C

84 kmph.

D

87 kmph.

Soln.
Ans: a

The speed of B is 55/1 = 55 km/h. So, the speed of A = \${17 × 55}/11\$ = 85 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 13km/h is 19sec, whereas the time it takes to cross the other man running at 26km/h is 20sec. What is the speed of the train?

A

273km/h.

B

274km/h.

C

272km/h.

D

275km/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 - 13) × 19\$. It should equal the length obtained from the data for the second man. So \$(v - 13) × 19\$ = \$(v - 26) × 20\$. Please note that we have not converted seconds to hours because that factor will ultimately cancel away. Solving for v we get 273km/h. 