A person covers the different distances by train, bus, and car in the ratio of 4 : 3 : 2. The ratio of the fair is 1 : 2 : 4 per km. The total expenditure as a fair is Rs 720. Find the total expenditure as fair on the train.

Given:

Distances covered by train, bus, and car are in the ratio 4:3:2.

Fares per km for train, bus, and car are in the ratio 1:2:4.

Total expenditure as a fare is Rs 720.

Concept:

We need to find the total expenditure as a fare on the train.

Calculation:

Let the distances covered by train, bus, and car be 4x, 3x, and 2x km respectively.

Let the fares per km for train, bus, and car be y, 2y, and 4y respectively.

Total expenditure = (Distance by train × Fare per km for train) + (Distance by bus × Fare per km for bus) + (Distance by car × Fare per km for car)

We have,

⇒ 720 = (4x × y) + (3x × 2y) + (2x × 4y)

⇒ 720 = 4xy + 6xy + 8xy

⇒ 720 = 18xy

⇒ xy = 720 / 18

⇒ xy = 40

Total expenditure as fare on the train = Distance by train × Fare per km for train

⇒ Total expenditure as fare on the train = 4x × y

⇒ Total expenditure as fare on the train = 4 × 40

⇒ Total expenditure as fare on the train = 160

∴ The total expenditure as fare on the train is Rs 160.