# Distance and Time Quiz Set 006

### Question 1

Two cars, A and B, start to move towards each other. If they meet when A has travelled \$(1/9)\$th of the distance, what is the ratio of the speed of B to the speed of A?

A

8.

B

9.

C

7.

D

10.

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/9)/u = ({8L}/9)/v\$. The ratio \$v/u\$ = 8.

### Question 2

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 3

Bus X travels 50% faster than bus Y. They start together and meet at the same time after travelling a distance of 30km. What is the speed of the bus X, if the bus Y wasted 5 hours during its journey?

A

2 kmph.

B

3 kmph.

C

5 kmph.

D

4 kmph.

Soln.
Ans: a

Let the speed of bus X be x, and of Y be 3x/2. The difference in the times taken by them is \$30/x - 30/({3x}/2)\$ = 5, which becomes 30 × \$1/{3x}\$ = 5. Solving, we get x = 2 km/h.

### Question 4

Two steamers X and Y travel towards a destination 192 km away. If Y travels 2 times faster than X, then it reaches 16 hours early. What is the speed of X?

A

6 kmph.

B

7 kmph.

C

5 kmph.

D

8 kmph.

Soln.
Ans: a

Let x be the speed of X, then the speed of Y is 2x. So \$192/x - 192/{2 × x} = 16.\$ Solving, we get x = 6 km/h.

### Question 5

Speeds of A and B are in the ratio 7 : 2. What is the speed of A if B can cover a distance of 6 Km in 1 hour?

A

21 kmph.

B

22 kmph.

C

20 kmph.

D

23 kmph.

Soln.
Ans: a

The speed of B is 6/1 = 6 km/h. So, the speed of A = \${7 × 6}/2\$ = 21 km/h.