Two-thirds of a certain distance was covered at the speed of 45 km/h, one-fourth at the speed of 60 km/h and the rest at the speed of 75 km/h. Find the average speed per hour for the whole journey. (correct to 2 decimal places)

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SSC CGL 2022 Tier-I Official Paper (Held On : 01 Dec 2022 Shift 4)
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  1. 51.25 km/h
  2. 45.75 km/h
  3. 58.25 km/h
  4. 49.77 km/h

Answer (Detailed Solution Below)

Option 4 : 49.77 km/h
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Detailed Solution

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Given:

2/3 of journey = 45 kmph

1/4 of journey = 60 kmph

(1 - 2/3 - 1/4 = 1/12) of journey = 75 kmph

Formula:

Average speed = Total distance/Total time

Calculation:

Let total distance of journey be a km.

Time taken for 2/3 of journey = 2a/135 hours

Time taken for 1/4 of journey = a/240 hours

Time taken for 1/12 of journey = a/900 hours

Total time taken for a km = 2a/135 + a/240 + a/900 = 217a/10800 hours

∴ Average speed = a/(217a/10800) = 49.77kmph

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