Airtel, a GSM service provider, offers a post-paid plan called Airtel One for its customers, with the tariff details shown below. Mohan made an STD call, within 100 km, for 30 minutes and spent 100 minutes on local calls, split 30% on landline, 40% on GSM and 30% on Airtel. Rohan made an STD call, within 150 km, for 18 minutes and spent 120 minutes on local calls, split 30% on GSM, 40% on landline and 30% on Airtel. Who spent more on calls that month?
Show Hint
Work out each person's local call cost first using the tariff table, then add the STD leg using the rate band that fits their distance.
Instead of listing every combination, find the worst case for Mohan, his highest possible spend, and the best case for Rohan, his lowest possible spend, then compare the two.
Mohan: local charges are fixed at $130 = 30(2)+40(1)+30(1)$ for the landline, GSM and Airtel shares. His STD leg of 30 minutes costs at most $30 \times 2 = 60$ if it is charged at the landline rate, so his highest possible total is $130+60=190$.
Rohan: local charges are fixed at $168 = 36(1)+48(2)+36(1)$ for his GSM, landline and Airtel shares. His STD leg of 18 minutes costs at least $18 \times 1.5 = 27$ if it is charged at the Airtel or GSM rate, so his lowest possible total is $168+27=195$.
Both spent the same amount: this cannot hold, since Rohan's lowest total, 195, already beats Mohan's highest total, 190, so their bills can never tie.
Cannot be determined: even without knowing the exact network for either STD call, the bounds show Rohan always spends more, so the comparison is fully determined.
Rohan's minimum bill of Rs. 195 is still higher than Mohan's maximum bill of Rs. 190, so Rohan spent more under every possible reading of the STD rate.
Let's summarize:
Mohan's bill lies between Rs. 175 and Rs. 190.
Rohan's bill lies between Rs. 195 and Rs. 201.
The two ranges never overlap, so Rohan always spends more.
