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.
Answer & explanation
Correct answer: option 1
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:
$720 \times \frac{2}{9} = 160$