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Unitary Method Test - 1

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Unitary Method Test - 1
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Weekly Quiz Competition
  • Question 1
    1 / -0

    Two person’s P and Q start at the same time from city A for city B, 80 km away. P travels 6 km/h slower than Q. Q reaches city B and at once turns back meeting P, 14 km from city B. What is speed of P?

    Solution

    AB = 80 km, BC = 14 km, 

    AC = (80 – 14) km = 66km

    Let the speed of P be x kmph so that speed of Q is (x+6) kmph. Time for P to cover a distance AC and time for Q to cover (AB+BC) are equal.

    ∴ 94/x+6 = 66/x

    94 x = 66 x + 396

    28 x = 396

    x = 14.1 km/h

     

  • Question 2
    1 / -0

    Two stations A and B are 170 km apart on a straight line. One train starts from A at 6 a.m. and travels towards B at 30 km/h. Another train starts from B at 7 a.m. and travels towards A at a speed of 40 km/h. At what time will they meet?

    Solution

    Suppose they meet x hours after 6 a.m.

    Distance covered by A in x hours = 30 x km.

    Distance covered by B in (x - 1) hours = 40(x - 1) km.

    = 30x + 40(x-1) = 170

    = 70x = 210

    = x = 3

    So, they meet at 9 am

     

  • Question 3
    1 / -0

    Out of a total distance covered of 300 km, first half is covered at the speed of 50 km / hr and the remaining half is covered at 25 km/hr. Find the total time taken to cover the whole journey. 

    Solution

    Time taken to cover first 100 Km at 50km/h = 100/50 = 2
    Time taken to cover last 100 Km at 25km/h = 100/25 = 4
    Total time taken to cover 300 Km =  2 + 4 = 6 hrs

     

  • Question 4
    1 / -0

    A train travels 102.5 km/hr. How many meters will it travel in 20 minutes? 

    Solution

    Speed of train = 102.5 km/h
    Train travel in 20 minutes  102.5 × 20/60
    = 34.16 km
    ⇒34.16 km = 34.16 × 1000m = 34160 m

     

  • Question 5
    1 / -0

    What is the distance travelled at the speed of 50 km/hr for 1/5 hours?

    Solution

    Distance = Speed × Time

    50 × 1/5 = 50 × 1/5 = 10km

     

  • Question 6
    1 / -0

    A train 300 m long is running at a speed of 54 km/hr. In what time will it pass a bridge 150 m long?

    Solution

    Formula for converting from km/hr to m/s= X km/hr = (x × 5/18) m/s

    Therefore,

    Speed = (54 × 5/18) m/sec = 16m/sec

    Total distance to be covered =(300 + 150)m = 450 m
    Formula for finding time =(Distance/Speed)

    ∴ Required Time = 450/15 sec =  30 sec

     

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