Q1.
For how many km will the fare be ₹130?
Answer
For a journey of n km (with n ≥ 2) the fare is ₹25 + 15(n − 2) = ₹(15n − 5).
15n − 5 = 130
15n = 135
n = 9 km
15n = 135
n = 9 km
Check the other way: for 9 km the meter charges ₹25 for the first 2 km and ₹15 for each of the remaining 7 km: 25 + 15 × 7 = 25 + 105 = ₹130. ✓
Why the formula reads 15n − 5 and not 15n + 25: the ₹15 rate does not start until after 2 km, so it applies to (n − 2) km, giving 25 + 15n − 30 = 15n − 5. The −5 is what is left of the base fare once the two free kilometres have been paid for at the higher rate. This also explains why the rule is stated only for n ≥ 2 — for a 1 km ride the fare is ₹25, not 15(1) − 5 = ₹10.
Check it yourself: use the rule for n = 2: 15(2) − 5 = ₹25, which agrees with the table. The formula stitches on correctly at the point where it starts to apply.