# Distance and Time Quiz Set 005

### Question 1

Speeds of A and B are in the ratio 11 : 4. What is the ratio of the times that they will take to cover a distance of 100 km?

A

4 : 11.

B

11 : 4.

C

4 : 100.

D

100 : 11.

Soln.
Ans: a

Let the speeds be 11x and 4x. The times they take to cover 100 km are \$100/{11x}\$ and \$100/{4x}\$. The ratio would be 4 : 11.

### Question 2

A train takes 1 hours less if its speed is increased by 4 km/hr. What is the normal speed if the distance is 3km?

A

2.

B

3.

C

5.

D

4.

Soln.
Ans: a

Let the normal speed be x km/hr. We have been given \$3/x\$ - \$3/{x + 4}\$ = 1. This translates to the quadratic equation \$1x^2 + 4x - 12 = 0\$, which can be solved to obtain x = 2 as the answer. If you don't want to solve the equation, then you can put each option into this equation and check that way. But this trick will work only if all the options have some numerical value.

### Question 3

A car is moving at a speed of 54 kmph. What is the speed in m/s?

A

15 m/s.

B

16 m/s.

C

14 m/s.

D

17 m/s.

Soln.
Ans: a

We know 1kmph = \$5/18\$ m/s. So 54kmph = \$5/18 × 54\$ = 15 m/s.

### Question 4

A vehicle travels 50% of its distance at 6 km/h, and the remaining 50% at 14 km/h. What is the total distance, if it travelled for a total duration of 40 hours?

A

336 km.

B

337 km.

C

335 km.

D

338 km.

Soln.
Ans: a

Let 2x be the actual duration of the journey. Then, \$x/6 + x/14 = 40\$. Solving for x we get x = 168, and so, 2x = 336 km.

### 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 3km/h is 14sec, whereas the time it takes to cross the other man running at 20km/h is 15sec. What is the speed of the train?

A

258km/h.

B

259km/h.

C

257km/h.

D

260km/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 - 3) × 14\$. It should equal the length obtained from the data for the second man. So \$(v - 3) × 14\$ = \$(v - 20) × 15\$. Please note that we have not converted seconds to hours because that factor will ultimately cancel away. Solving for v we get 258km/h.