Q1.
What is the cost for travelling 15 km? For how many kilometres will the cost of the journey be ₹700?
Answer
The cost function is C(d) = 100 + 60d.
C(15) = 100 + 60(15)
= 100 + 900
= ₹1000
= 100 + 900
= ₹1000
Now run the machine backwards.
100 + 60d = 700
60d = 600
d = 10 km
60d = 600
d = 10 km
Why the ₹100 must be taken out first: the ₹100 is a fixed charge that does not depend on the distance — it is the value of C at d = 0. Only the remaining ₹600 was bought at the rate of ₹60 per km. Dividing 700 by 60 without removing the fixed part would give 11.67 km, which is wrong. In the language we are building: 100 is the y-intercept and 60 is the slope.
Check it yourself: C(10) = 100 + 600 = ₹700 ✓, and going from 10 km to 15 km adds 5 × ₹60 = ₹300, taking ₹700 to ₹1000.