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CTET Maths - Time and Work

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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?

  • Option : C
  • Explanation : 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.
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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?

  • Option : D
  • Explanation :
    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.
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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.

  • Option : A
  • Explanation :
    Let fixed interval be x
    ∴
    ⇒ (5)6 + (5 - x)4 + (5 - 2x)3 = 60
    ⇒ 30 + 20 - 4x + 15 - 6x = 60
    ⇒ x = hour.
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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?

  • Option : C
  • Explanation :
    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.
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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?

  • Option : C
  • Explanation :
    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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