CTET Maths MCQ - Time and Work

Refer to the graph below and answer the questions that follow.
The engine of the new car Palio brought by Fiat in the market follows certain mileage characteristics as shown in the diagram below:

Vijay bought the new car Palio and filled exactly 10 litres in his car. He goes at a speed of 40 km/hr for first 20 km and then at a speed of 60 km/hr for next 60 km and driving at a constant speed reaches his destination which was 115 km away from his starting point.

26 In the above question, if Vijay had travelled at a constant average speed rather than changing his speed, taking the same minimum time, then what would have been the approximate saving in the fuel consumed?

Total distance travelled = 115 km

27 Two men, A and B, run a 4 km race on a circular course of

km. If their speeds are in the ratio of 5:4, how often does the winner pass the other

When A runs 5 rounds, B runs 4 rounds (ratio of speeds)
∴ A passes B each time A has run 5 round or

Hence A passes B thrice.

28 In a 2 km race on a circular course of of a km. A overlaps B in the middle of his 6th round. By what distance will A win at the same rate of running?

29 A and B start from the same point to run in opposite directions round a circular path 550 yards in length, A giving B a start of 100 yards. They pass each other when A has run 250 yards. Who will come first to the starting point and at what distance will they be apart?

When A has run 250 yards, B should have run
550 - 250 = 300 yards.
∴ Bruns 300 - 100 = 200 yards in the same time taken by A to run 250 yards.
∴ Ratio of the speeds of A and B = 250 : 200 = 5 : 4
If speed of A is 5x yards per minute, then speed at B = 4x yards/min.
Time taken by B to reach the starting point

Hence B is 10 yards behind A.

30 A runs

times faster than B. A gives B a start of 120 metres. How far must the winning post be so that it may be a dead heat?

Speeds of A and B are as

In a race of 11 metres, A gain 11- 8 = 3 metres over B.
To gain 120 metres, race must be of
= 120 x 11/3 = 440 metre