# Distance and Time Quiz Set 002

### Question 1

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 2

A cyclist travels at a speed of 2km/h. Had he travelled at 9km/h he would have covered a distance of 42 km more. What is the total distance travelled by him?

A

12 km.

B

13 km.

C

11 km.

D

14 km.

Soln.
Ans: a

By the given problem, the time is same for both cases. If the total distance covered by him at 2km/h is x, then, \$x/2 = {x + 42}/9\$. Solving, we obtain x = 12 km.

### Question 3

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 4

A boy goes to his school at an average speed of 2 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

\$2{2/5}\$ km/h.

B

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

C

1 km/h.

D

\$3{6/7}\$ km/h.

Soln.
Ans: a

If u and v are the to and fro speeds, then the standard formula is \${2uv}/{u + v}\$ = \${2 × 2 × 3}/{2 + 3}\$ = \${12/5}\$, which is same as: \$2{2/5}\$ km/h.

### Question 5

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.