Engine Operational
GATE CH 2020 (with Solutions).pdf

Q9

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The distance between Delhi and Agra is 233 km. A car P started travelling from Delhi to Agra and another car Q started from Agra to Delhi along the same road 1 hour after the car P started. The two cars crossed each other 75 minutes after the car Q started. Both cars were travelling at constant speed. The speed of car P was 10km/hr more than the speed of car Q. How many kilometers the car Q had travelled when the cars crossed each other?

Options

  1. A.
    116.5
  2. B.
    88.2
  3. C.
    66.6
  4. D.
    75.2

Answer

D

Solution

Given : The distance between Delhi and Agra is 233 km.
..
Car P→←CarQ Car P and Q crossed each other 75 minutes after the car Q started. Let x km be the distance covered by CarQ in 75 minutes.
/textSpeed/textat/textCarQ=/frac/frac/fracx7560kmhr=/frac/frac4x5kmhr∴ /text{Speed} /text{at} /text{CarQ} = /frac{/frac{/frac{x}{75}}{60km}}{hr} = /frac{/frac{4x}{5km}}{hr}
/textSpeed/textat/mathrmCarP=/frac4x5+/frac10kmhr∴ /text{Speed} /text{at} /mathrm{Car} P = /frac{4x}{5}+/frac{10km}{hr}
..
..
∴ The distance covered by car P till the point of crossing =(233−x) The distance travelled by carQ is given by ()
(233x)=/frac/frac944x5+10(233-x) = /frac{/frac{9}{44x}}{5}+10
x=75.2kmx = 75.2km
Hence, the correct option is (D).

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