CTET Maths MCQ - Time and Work

1 Two men, A and B, run a 4 km race on a circular course of 1/4 km. If their speeds are in the ratio of 5:4, how often doe's 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 rounds or 5 x 1/4 = 5/4km. = 1 1/4km
1 1/4km is contained in 4 km 3 times. Hence A passes B thrice.

2 Meera paints walls for a living. She sometimes has Ashok to work with her. Meera takes 2 days to paint a 10 ft by 10 ft wall. Ashok takes 3 days to do the same job. Meera has to pay Ashok for his work on a per day basis, so she'd rather do without him. Meera has recently got a contract to paint the walls and ceiling of a room of dimensions 10 ft by 15 ft and a height of 10 ft. She had promised to do the job within 9 days. For how many days does she need to employ Ashok?

Total area to be painted
= 10 x 15 (ceiling) + 2 x 10 x 10 (wall) + 2 x 10 x 15 (wall)
= 650 sq.ft
In one day Meera can paint 10 x 10/2 = 50 sq ft
Ashok can paint 10 x 10/3 = 100/3 sq ft,
So, together they can paint 250/3 sq ft per day.
Let number of days Ashok works be x.
Work done in 9 days = 50(9 - x) + (250/3)x = 650
∴ 450 - 50x + (250x/3) = 650
⇒ 250x/3 = 200
⇒ x = 6 days.

3 3 pipes can fill a reservoir in 10, 15 and 20 hours respectively. If the three taps are opened one after another in the given order, with a certain fixed time gap between them, the reservoir fills in 5 hours. The time gap will be.

Let fixed interval be x
∴

⇒ (5)6 + (5 - x)4 + (5 - 2x)3 = 60
⇒ 30 + 20 - 4x + 15 - 6x = 60
⇒ x =

hour.

4 Two pipes Aand B can fill a tank in 8 hours. If only pipe A is open, then it would take 4 hours longer to fill the tank. How much longer would it take if only pipe B is open?

Let pipe B alone take b hours longer than if both A and B were open.
8 = √(4 × x)
⇒ 64 = 4 × x
⇒ x = 16 hours.
Alternatively
Part filled if both A and B are open = 1/8
Part filled if only A is open = 1/12
∴ Part filled if only B is open = (1/8) - (1/12) = 1/24
∴ B alone would take 24 hours, i.e., B alone would take 24 - 8 = 16 hours longer to fill the tank.

5 A barrel full of beer has 2 taps, one midway which draws a litre in 6 minutes and the other at the bottom which draws a litre in 4 minutes. The lower tap is normally used after the level of beer in the barrel is lower than midway. The capacity of the barrel is 36litres. A new assistant opens the lower tap when the barrel is full and draws out some beer. As a result the lower tap has been used 24 minutes before the usual time. For how long was the beer drawn out by the new assistant?

Top tap is operational till 18 litres is drawn out.
∴ Time after which the lower tap is usually open = 18 x 6 = 108 minutes.
∴ Time after which it is open now = 108 - 24 = 84 minutes.
∴ Litres d rawn = 84/16 = 14 litres
∴ 18 - 14 = 4 litres
were drawn by the new assistant.
∴ Time = 4 x 4 = 16 minutes.

Alternatively
Upper tap was not used for 24 minutes.
∴ Litres drawn = 24/6 = 4 litres.
∴ Beer was drawn for 4x 4 = 16 minutes.

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CTET Maths MCQ - Time and Work

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