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An auto driver charges fixed fair for first 20 km. After 20 km he charges per km. If the driver charges 30 km for Rs. 400 and charge 40 km for Rs. 600. What is the fair of auto if the auto covers 74 km distance?

An auto driver charges fixed fair for first 20 km. After 20 km he charges per km. If the driver charges 30 km for Rs. 400 and charge 40 km for Rs. 600. What is the fair of auto if the auto covers 74 km distance? Correct Answer Rs. 1280

Given,

Fair of auto to cover 30 km distance = Rs. 400

Fair of auto to cover 40 km distance = Rs. 600

Calculation:

Let the fixed charge be Rs. x and thereafter charge per km be Rs. y

According to the question

x + 10y = 400      ---- (1)

x + 20y = 600      ---- (2)

Subtract equation (1) from equation (2)

10y = 200

⇒ y = 20

From equation (1)

x + 20 × 10 = 400

⇒ x + 200 = 400

⇒ x = 400 – 200

∴ x = 200

Fixed charge for first 20 km is Rs. 200

Per km charge after 20 km is Rs. 20

Total fair if the auto covers 74 km distance = x + 54y

⇒ 200 + 54 × 20

⇒ 200 + 1080

⇒ 1280

∴ Total fair of auto to cover 74 km distance is Rs. 1280.

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