# Distance and Time Quiz Set 011

### Question 1

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 4 km/h and 8 km/h, and B started 1 hour late?

A

16 km.

B

17 km.

C

15 km.

D

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

Soln.
Ans: a

If the distance between them is L, they meet after travelling L/2. Equating the times they travelled, \$L/{2 × 4} = L/{2 × 8} + 1\$. Solving for L we get L = 16 km.

### Question 2

A train takes 3 hours less if its speed is increased by 2 km/hr. What is the normal speed if the distance is 12km?

A

2.

B

3.

C

5.

D

4.

Soln.
Ans: a

Let the normal speed be x km/hr. We have been given \$12/x\$ - \$12/{x + 2}\$ = 3. This translates to the quadratic equation \$3x^2 + 6x - 24 = 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 cyclist travels at a speed of 4km/h. Had he travelled at 6km/h he would have covered a distance of 10 km more. What is the total distance travelled by him?

A

20 km.

B

21 km.

C

19 km.

D

22 km.

Soln.
Ans: a

By the given problem, the time is same for both cases. If the total distance covered by him at 4km/h is x, then, \$x/4 = {x + 10}/6\$. Solving, we obtain x = 20 km.

### Question 4

A train passes two persons walking in the same direction as the train. The time it takes to move past the man running at 6km/h is 18sec, whereas the time it takes to cross the other man running at 8km/h is 19sec. What is the speed of the train?

A

44km/h.

B

45km/h.

C

43km/h.

D

46km/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 - 6) × 18\$. It should equal the length obtained from the data for the second man. So \$(v - 6) × 18\$ = \$(v - 8) × 19\$. Please note that we have not converted seconds to hours because that factor will ultimately cancel away. Solving for v we get 44km/h.

### Question 5

Two steamers X and Y travel towards a destination 510 km away. If Y travels 6 times faster than X, then it reaches 5 hours early. What is the speed of X?

A

85 kmph.

B

86 kmph.

C

84 kmph.

D

87 kmph.

Soln.
Ans: a

Let x be the speed of X, then the speed of Y is 6x. So \$510/x - 510/{6 × x} = 5.\$ Solving, we get x = 85 km/h.

Updated on 2020-02-07. Published on: 2016-05-06

Posted by Parveen(Hoven),
Aptitude Trainer