Question

A man travels 360 km in 4 hrs, partly by
air and partly by train. If he had travelled
all the way by air, he would have saved th
of the time he was in train and would have
arrived at his destination 2 hours early.
Find the distance he travelled by air and
train​

Answer 1

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Correct question - A man travels 400 kms in 4 hours partly by air and partly by train. If he had travelled all the way by air, he would have saved (4/5)th of the time he was in train and would have arrived his destination 2 hours early. Find the distance he travelled by train.

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Given -

Distance = 360 km,

Time = 4 hours

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Calculating-

Obviously, 4/5 of total time in train = 2 hours

∴ Total time in train = 5/4×2 = 5/2 hours

➠Total time to cover 400 km is 4 hours

Time spent in travelling by air

➠ 4- 5/2 = 8-5/2

➠ 3/2 hours

If 400 kms is travelled by air, then time taken = 2 hours

➠ In 2 hours, distance covered by air = 400 kms

➠In 3/2 hours distance covered

= 400/2 × 3/2

= 300 kms

➠Distance covered by the train

= 400 – 300 = 100 kms.

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Answer 2

Correct Question :- A man travels 360 km in 4 hrs, partly by air and partly by train. If he had travelled all the way by air, he would have saved (4/5)th of the time he was in train and would have arrived at his destination 2 hours early.

Find the distance he travelled by air and train ? (Nice Question .)

Solution :-

Given That :-

→ Total Distance = 360km.

→ Total Time taken by air & Train = 4 Hours.

→ Time All the way by air = (Total Time - Saving Time) = 4 - 2 = 2 Hours.

So, we can say That ,

→ Speed By air = (Distance/Time) = (360/2) = 180km/h. --------- Equation (1).

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Now, we have given that, If he had travelled all the way by air, he would have saved (4/5)th of the time he was in train.

So, we can say That,

→ (4/5) * Train = 2 Hours .

→ Train = (2*5/4) = (5/2) Hours.

Hence,

→ Time Taken by air = Total Time - Time Taken by Train .

→ Time Taken by air = (4) - (5/2)

→ Time Taken by air = (8 - 5) / 2

→ Time Taken by air = (3/2) Hours. ---------- Equation (2).

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From Equation (1) & (2) , we get,

→ Total Distance Covered By air = Speed * Time.

→ Total Distance Covered By air = 180 * (3/2)

→ Total Distance Covered By air = 270km.

And,

→ Total Distance Covered By Train = 360 - 270 = 90km.

ஃ The Man Travelled 270km by Air and 90km by Train.