Observe that the total fare for a travel of n km will be ₹25 + 15 × (n − 2) = 15n − 5, when n ≥ 2.
For how many km will the fare be ₹130?
Answer: 15n − 5 = 130 gives n = 9. The fare is ₹130 for 9 km.
Step-by-step solution
Given: Auto-rickshaw fare: ₹25 for the first 2 km, then ₹15 per km; Fare for n km (n ≥ 2) = ₹(15n − 5)
Idea: Set the fare expression equal to 130 and solve the linear equation for n.
- 15n − 5 = 130½ mark
- 15n = 135½ mark
- n = 135 ÷ 15 = 9. The fare is ₹130 for 9 km.1 mark
The fare will be ₹130 for a travel of 9 km.
Check: 25 + 15 × (9 − 2) = 25 + 105 = 130 ✓.
Answer to write in the exam
15n − 5 = 130
15n = 135 ⇒ n = 9
∴ The fare is ₹130 for 9 km
Common mistakes that cost marks
- Dividing 130 by 15 directly (about 8.7). The starting ₹25 for the first 2 km must be accounted for.
- Writing 15n = 125 by subtracting 5 instead of adding it.
- Answering 7 km: 7 is the number of kilometres after the first 2; the whole trip is 9 km.
How this can come in the exam
MCQ (1 mark)
A courier charges ₹(8w + 20) for a parcel of w kg. A parcel cost ₹116. Its weight is
- 12 kg
- 14.5 kg
- 17 kg
- 10 kg
Show answer
(A) 12 kg
8w + 20 = 116 ⇒ 8w = 96 ⇒ w = 12.
Short answer (2 marks)
With the same auto-rickshaw fares, Priya paid ₹205. How far did she travel?
Show answer
15n − 5 = 205 ⇒ 15n = 210 (1 mark) ⇒ n = 14 km (1 mark).Try one yourself
With the same fares, for how many km will the fare be ₹265?
Show answer
15n − 5 = 265 ⇒ 15n = 270 ⇒ n = 18 km.
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