An auto-rikshaw fare starts at ₹25 and remains the same for the initial 2 km. Then it increases by ₹15 per km. What will be the fare for a travel of 10 km?
Step-by-step solution
To find: The fare for 10 km
Idea: The first 2 km cost a fixed ₹25. Only the kilometres after the first 2 are charged at ₹15 each.
- For 10 km, the extra kilometres beyond the first 2 are 10 − 2 = 8 km.1 mark
- Fare = 25 + 15 × 8 = 25 + 120 = ₹145.1 mark
- Table of fares:
Km travelled 1 2 3 4 5 6 Fare (₹) 25 25 25 + 1 × 15 = 40 25 + 2 × 15 = 55 25 + 3 × 15 = 70 25 + 4 × 15 = 85 - In general, for n km (n ≥ 2): fare = 25 + 15(n − 2) = 25 + 15n − 30 = ₹(15n − 5). The fare is a function of the distance. Check: 15 × 10 − 5 = 145 ✓.1 mark
Check: Formula 15n − 5 at n = 10: 150 − 5 = 145 ✓. At n = 6: 85, which matches the table ✓.
Answer to write in the exam
Distance after the first 2 km = 10 − 2 = 8 km
Fare = 25 + 15 × 8 = 25 + 120
In general, fare for n km (n ≥ 2) = 25 + 15(n − 2) = ₹(15n − 5)
∴ Fare for 10 km = ₹145
Common mistakes that cost marks
- Charging ₹15 for all 10 km: 25 + 150 = ₹175. The first 2 km are already covered by the ₹25.
- Using 10 × 15 = ₹150 and forgetting the starting fare.
- Writing the general fare as 25 + 15n instead of 25 + 15(n − 2).
How this can come in the exam
A taxi charges ₹50 for the first 3 km and ₹12 for each km after that. The fare for 13 km is
- ₹156
- ₹170
- ₹206
- ₹120
Show answer
(B) ₹170
50 + 12 × (13 − 3) = 50 + 120 = ₹170.
A parking lot charges ₹30 for the first hour and ₹20 for every hour after that.
(i) Find the charge for 1 hour and for 4 hours. (ii) Write the charge for h hours (h ≥ 1). (iii) Find the charge for 9 hours. (iv) A driver paid ₹250. How long did she park?
Show answer
(i) ₹30; 30 + 20 × 3 = ₹90 (1 mark). (ii) 30 + 20(h − 1) = ₹(20h + 10) (1 mark). (iii) 20 × 9 + 10 = ₹190 (1 mark). (iv) 20h + 10 = 250 ⇒ h = 12 hours (1 mark).Try one yourself
Using the same auto-rickshaw fares, find the fare for 7 km and for 15 km.
Show answer
15 × 7 − 5 = ₹100; 15 × 15 − 5 = ₹220.
More questions like this
- 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? - A student has ₹500 in her savings bank account. She gets ₹150 every month as pocket money. How much money will she have at the end of every month from the second month onwards? Find a linear expression to represent the amount she will have in the nth month.
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- Suppose the length of a rectangle is 13 cm. Find the area if the breadth is (i) 12 cm, (ii) 10 cm, (iii) 8 cm. Find the linear pattern representing the area of the rectangle.
- Suppose the length of a rectangular box is 7 cm and breadth is 11 cm. Find the volume if the height is (i) 5 cm, (ii) 9 cm, (iii) 13 cm. Find the linear pattern representing the volume of the rectangular box.