Question

The taxis plying in Wasseypur have the following fare structure: Rs 20 for the first two kilometers, Rs 5 for every km in excess of 2 km and up to 10 km, and Rs 8 for every km in excess of 10 km. Bullock carts on the other hand charge Rs 2 per km. Sardar Khan takes a taxi from the Wasseypur railway station to his home. On the way, at a distance of 14 km from the railway station, he meets Faizal Khan, and gets down from the taxi to talk to him. Later he takes a bullock cart to reach his home. He spends a total of Rs 102 to reach his home from the railway station. How far is his home from the railway station (in kilometers)?

• A. 17
• B. 18
• C. 19
• D. 20
• E. 21

Hint:

Break piecewise fare structures into segments and compute cost for each segment separately.
When a trip is split, compute each leg's cost independently and sum them.

Answer 1

The Correct Option is C

Step 1: Let the distance from the railway station to Sardar's home be \(D\) km. He takes a taxi from station to the 14 km mark, then a bullock cart from the 14 km mark to his home, a remaining distance of \(D-14\) km.
Step 2: Compute the taxi fare for 14 km. Fare structure:
First 2 km: Rs \(20\).
Next up to 8 km (i.e. from 2 to 10): \(8\times 5=40\) rupees.
Beyond 10 km: rate Rs \(8\) per km. For 14 km total, excess beyond 10 is \(4\) km so cost \(4\times 8=32\).
Total taxi fare \(=20+40+32=92\) rupees.
Step 3: Bullock cart charges Rs \(2\) per km for remaining \(D-14\) km, so cart cost \(=2(D-14)\).
Step 4: Total spent is \(92+2(D-14)=102\). Solve: \[ 2(D-14)=102-92=10⇒ D-14=5⇒ D=19. \]