Exercise : 1


1. A car finishes a journey in ten hours at the speed of 80 km/hr. If the same distance is to be covered in eight hours how much more speed does the car have to gain?
(a) 8 km/hr
(b) 10 km/hr
(c) 12 km/hr
(d) 16 km/hr
(e) None of these
Ans.e

Distance covered by the car = 80 × 10 = 800 km

\ Speed = 8008 = 100 km/hr

\ Speed gain = 100 – 80 = 20 km/hr

2. Two cars A and B are running towards each other from different places 88 km apart. If the ratio of the speeds of the cars A and B is 5 : 6 and the speed of the car B is 90 km per hour then after how long will the two meet each other?
(a) 2263 minutes
(b) 24 minutes
(c) 32 minutes
(d) 36 minutes
(e) None of these
Ans.c

Speed of the car A = 56 × 90 = 75 km/hr

\ Reqd time = \(\frac{88}{90 + 75} \times 60 = 32 \; minutes\)

3. Train ‘A’ leaves Mumbai Central for Lucknow at 11 am, running at the speed of 60 kmph. Train ‘B’ leaves Mumbai Central for Lucknow by the same route at 2 pm on the same day, running at the speed of 72 kmph. At what time will the two trains meet each other?
(a) 2 am on the next day
(b) 5 am on the next day
(c) 5 pm on the next day
(d) 2 pm on the next day
(e) None of these
Ans.b

Distance covered by train A before the train B leaves

Mumbai Central = 60 × 3 = 180 km

\ Time taken to cross each other = 18012 = 15 hours

\Reqd time = 2pm + 15 = 5 am on the next day

4. A motor starts with the speed of 70 kmph with its speed increasing every two hours by 10 kmph. In how many hours will it cover 345 kms?
(a) 214 hours
(b) 412 hours
(c) 4 hours 5 minutes
(d) Cannot be determined
(e) None of these
Ans.b

Distance covered in first two hours = 70 × 2 = 140 km

Distance covered in next two hours = 80 × 2 = 160 km

Distance covered in first four hours

140 + 160 = 300 km

Remaining distance = 345 – 300 = 45 km.

Now, this distance will be covered at the speed of 90 km/hr.

∴ Time taken = 4590 = 12 hour.

Total time= 4 + 12 = 412 hour.

5. A boat takes 3 hours to travel from place M to N down stream and back from N to M upstream. If the speed of the boat instill water is 4 km/hr, what is the distance between the two places?
(a) 8 km
(b) 12 km
(c) 6 km
(d) Data inadequate
(e) None of these
Ans.d

Let the distance between M and N and the speed of current in still water be d km and x km/hr respectively.

According to the question, \(\frac{d}{4 + x} + \frac{d}{4 - x} = 3\)

In the above equation we have only one equation but two variables, hence, can’t be determined.

6. A boat has to travel upstream 20 km distance from point X of a river to point Y. The total time taken by boat in travelling from point X to Y and Y to X is 41 minutes 40 seconds. What is the speed of the boat?
(a) 66 km/hr
(b) 72 km/hr
(c) 48 km/hr
(d) Data inadequate
(e) None of these
Ans.d

Let x be the speed of the boat.
and y the speed of the current.

\(\frac{20}{x - y} + \frac{20}{x + y} = \frac{25}{36}\)

In this equation there are two variables, but only one equation, so, the value of ‘x’ cannot be determined.

7. The speed of a car increases by 2 km after every hour. If the distance travelled in the first hour was 35 km, what was the total distance travelled in 12 hours?
(a) 522 km
(b) 456 km
(c) 556 km
(d) 482 km
(e) None of these
Ans.e

This is the problem of arithmetic progression (AP) with the first term (a) = 35, common difference (d) = 2 and total no. of terms (n) = 12. The sum of this series will be total distance travelled.

Sum (Sn) = n2{2a + (n - 1)d} = 122{70 + 11 × 2}

= \(\frac{12 \times 92}{2} = 552 \; km\)

8. A boat covers a distance of 30 km downstream in 2 hours while it take 6 hours to cover the same distance upstream. If the speed of the current is half of the speed of the boat then what is the speed of the boat in km per hour?
(a) 15 kmph
(b) 5 kmph
(c) 10 kmph
(d) Data inadequate
(e) None of these
Ans.c

Here downstream speed = 15 km/hr and upstream speed = 5 km/hr

∴ Speed of the boat = \(\frac{15 + 5}{2} = 10 \; km/h\)

9. A man starts walking. He walked 2 km in the first hour. Then he walked two-thirds of the distance of the previous hour in each next hour. If he walked continuously then how long could he walk maximum?
(a) 60 km
(b) 6 km
(c) 12 km
(d) 8 km
(e) None of these
Ans.b

Required distance

= \(2\left[1 + \frac{2}{3} + \left(\frac{2}{3} \right)^{2} + \left(\frac{2}{3} \right)^{3} + .... \right]\)

= \(2 \times \frac{1}{1 - \frac{2}{3}} = 2 \times 3 = 6 \; km.\)

10. Starting with the initial speed of 30 km/hr, the speed is increased by 4 km/hour every two hours. How many hours will it take to cover a distance of 288 km?
(a) 4
(b) 6
(c) 12
(d) 8
(e) None of these
Ans.d

Hour Speed (km/h) Distance travelled (in km)

5

Hence, the required time = 8 hours