Distance and Time Quiz Set 020

Question 1

Bus X travels 50% faster than bus Y. They start together and meet at the same time after travelling a distance of 36km. What is the speed of the bus X, if the bus Y wasted 6 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 \$36/x - 36/({3x}/2)\$ = 6, which becomes 36 × \$1/{3x}\$ = 6. Solving, we get x = 2 km/h.

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 3 km/h and 9 km/h, and B started 1 hour late?

A

9 km.

B

10 km.

C

8 km.

D

4 km.

Soln.
Ans: a

If the distance between them is L, they meet after travelling L/2. Equating the times they travelled, \$L/{2 × 3} = L/{2 × 9} + 1\$. Solving for L we get L = 9 km.

Question 3

A train takes 5 hours less if its speed is increased by 12 km/hr. What is the normal speed if the distance is 120km?

A

12.

B

13.

C

11.

D

14.

Soln.
Ans: a

Let the normal speed be x km/hr. We have been given \$120/x\$ - \$120/{x + 12}\$ = 5. This translates to the quadratic equation \$5x^2 + 60x - 1440 = 0\$, which can be solved to obtain x = 12 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 4

Two trains start simultaneously. The first train moves from Hyderabad to Bangalore, whereas the second train moves from Bangalore to Hyderabad. After they meet at a point in between, they respectively take 36 hours and 25 hours to reach their destinations. What is the ratio of their speeds?

A

\${5/6}\$.

B

\${11/5}\$.

C

\${17/8}\$.

D

\${23/8}\$.

Soln.
Ans: a

If they take \$t_1 and t_2\$ hours respectively to reach their destinations, then the ratio of their speeds is \$√t_2 : √t_1\$. So we get \$√25 : √36\$, which gives 5 : 6, or \${5/6}\$.

Question 5

Speeds of A and B are in the ratio 7 : 8. What is the ratio of the times that they will take to cover a distance of 100 km?

A

8 : 7.

B

7 : 8.

C

8 : 100.

D

100 : 7.

Soln.
Ans: a

Let the speeds be 7x and 8x. The times they take to cover 100 km are \$100/{7x}\$ and \$100/{8x}\$. The ratio would be 8 : 7.