The cost of a journey is given by the linear function C(d) = 100 + 60d, where C indicates total cost in rupees and d the distance travelled in km. Let us make a table of values for d varying from 0 to 10 km and show how the cost increases for every km.
Answer: Costs for d = 0 to 10 km: ₹100, 160, 220, 280, 340, 400, 460, 520, 580, 640, 700. The cost rises by a fixed ₹60 for every km: this is linear growth.
Step-by-step solution
Given: C(d) = 100 + 60d
Idea: Put d = 0, 1, 2, …, 10 into 100 + 60d. Since d is multiplied by 60, each extra km adds exactly ₹60.
- Substitute each value of d, for example C(0) = 100, C(1) = 100 + 60 = 160, C(10) = 100 + 600 = 700:1 mark
Distance travelled, d (km) Cost, C (₹) 0 100 1 160 2 220 3 280 4 340 5 400 6 460 7 520 8 580 9 640 10 700 - Each time d increases by 1 km, the cost increases by the fixed amount ₹60 (160 − 100 = 60, 220 − 160 = 60, …).½ mark
- A quantity that increases by a fixed amount over equal intervals shows linear growth.½ mark
The cost goes 100, 160, 220, …, 700 rupees for 0 to 10 km, increasing by ₹60 for every km (linear growth).
Check: C(5) = 100 + 300 = 400, which matches the table ✓.
Answer to write in the exam
C(d) = 100 + 60d
d = 0, 1, 2, …, 10 → C = 100, 160, 220, 280, 340, 400, 460, 520, 580, 640, 700
Each increase of 1 km increases C by ₹60
∴ The cost shows linear growth of ₹60 per km
Common mistakes that cost marks
- Writing C(0) = 160 by forgetting that 60 × 0 = 0; at 0 km only the fixed ₹100 is charged.
- Saying the cost increases by ₹160 per km (confusing C(1) with the increase).
- Working out 60d + 100 as 160d.
How this can come in the exam
MCQ (1 mark)
For C(d) = 80 + 45d, the increase in cost for each extra km is
- ₹80
- ₹125
- ₹45
- ₹35
Show answer
(C) ₹45
The coefficient of d, 45, is the fixed increase per km.
Short answer (2 marks)
The charge for hiring a bicycle is H(t) = 20 + 15t rupees for t hours. Make a table for t = 0 to 4 and state the increase per hour.
Show answer
20, 35, 50, 65, 80 (1 mark). It increases by ₹15 per hour: linear growth (1 mark).Try one yourself
For C(d) = 50 + 35d, find the costs for d = 0, 2, 4, 6 and the increase per km.
Show answer
₹50, 120, 190, 260; ₹35 per km.
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- The cost of a journey is given by the linear function C(d) = 100 + 60d, where C indicates total cost in rupees and d the distance travelled in km.
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