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

160

Let the distances traveled by train, bus, and car be:

• Train = $4x\text{ km}$
• Bus = $3x\text{ km}$
• Car = $2x\text{ km}$

The fare per km is in the ratio:

• Train : Bus : Car = 1 : 2 : 4

So, the expenditure on each is proportional to:

• Train = $4x \times 1 = 4x$
• Bus = $3x \times 2 = 6x$
• Car = $2x \times 4 = 8x$

Thus, the ratio of expenditures is:

$4 : 6 : 8 = 2 : 3 : 4$

Total ratio:

$2 + 3 + 4 = 9$

Given the total fare = ₹720.

Train fare:

$720 \times \frac{2}{9} = 160$