For the same trip, a train ticket costs 60% more than a bus ticket. By what percentage is the bus ticket cheaper than the train ticket?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 37.5%
“More than” is measured on the bus fare, but “cheaper than the train ticket” is measured on the train fare, so the base changes.
Let the bus ticket cost Rs 100. The train ticket costs Rs 160
Difference \(=160-100=60\)
As a percentage of the train fare \(\displaystyle =\frac{60}{160}\times100=37.5\%\)
The bus ticket is 37.5% cheaper than the train ticket.
Why the other options are incorrect
Option (1) 60% — Incorrect. This keeps the bus fare as the base; the question compares with the train fare.
Option (2) 40% — Incorrect. 40% of Rs 160 is Rs 64, not the Rs 60 difference.
Option (4) 62.5% — Incorrect. This is the bus fare as a percentage of the train fare, \(\frac{100}{160}\), not how much cheaper it is.