Question

Under the 'Airtel One' postpaid plan, the monthly rental is Rs. 99, and call charges are billed on top of this rent based on the distance slab and the network used. A bill of Rs. 199 in a month is definitely not possible when you make only:

• A. 30 calls to Airtel on STD (500+ km) and 55 local calls in a month
• B. 16 calls to Airtel on STD (15 km) and 76 local calls in a month
• C. 10 STD calls (250 km) each to Airtel, GSM and landline respectively, and 30 local calls in a month
• D. 8, 4 and 7 calls to Airtel, GSM and landline respectively on STD (500+ km), and 55 local calls in a month

Hint:

Subtract the fixed rent from Rs. 199 first, then check which option's cheapest possible call cost still exceeds what remains.

Answer 1

The Correct Option is D

Step 1: Work out what the variable part of the bill must be.
The Airtel One plan carries a fixed monthly rent of Rs. 99. For the total bill to touch Rs. 199, the calls and local usage together must add up to \( 199 - 99 = 100 \) rupees in that month.

Step 2: List the call rates that apply.
Airtel to Airtel (on net) STD calls are billed at a flat \( Rs. 1.5 \) per call, no matter the distance slab. GSM STD calls cost \( Rs. 2.5 \) per call up to 250 km and \( Rs. 3 \) per call beyond 500 km. Landline STD calls cost \( Rs. 2.5 \) per call up to 250 km and \( Rs. 3.5 \) per call beyond 500 km. Local calls to Airtel or GSM numbers cost \( Rs. 1 \) per call, while local landline calls cost \( Rs. 2 \) per call.

Step 3: Check option A.
30 Airtel STD calls (500+ km) cost \( 30 \times 1.5 = Rs. 45 \). 55 local mobile calls cost \( 55 \times 1 = Rs. 55 \). Total \( = 45 + 55 = Rs. 100 \), which matches exactly, so a Rs. 199 bill is possible here.

Step 4: Check option B.
16 Airtel STD calls cost \( 16 \times 1.5 = Rs. 24 \). 76 local calls cost \( 76 \times 1 = Rs. 76 \). Total \( = 24 + 76 = Rs. 100 \), again an exact match, so this bill is also possible.

Step 5: Check option C.
10 STD calls each to Airtel, GSM and landline at 250 km cost \( (10 \times 1.5) + (10 \times 2.5) + (10 \times 2.5) = 15 + 25 + 25 = Rs. 65 \). The 30 local calls can be all mobile (\( 30 \times 1 = Rs. 30 \)) or all landline (\( 30 \times 2 = Rs. 60 \)), so the local charge lies between Rs. 30 and Rs. 60. Total spend lies between Rs. 95 and Rs. 125, and Rs. 100 sits inside that range, so this bill is possible too.

Step 6: Check option D.
8 Airtel, 4 GSM and 7 landline STD calls at 500+ km cost \( (8 \times 1.5) + (4 \times 3) + (7 \times 3.5) = 12 + 12 + 24.5 = Rs. 48.5 \). The 55 local calls cost between \( 55 \times 1 = Rs. 55 \) and \( 55 \times 2 = Rs. 110 \). So the total spend lies between \( 48.5 + 55 = Rs. 103.5 \) and \( 48.5 + 110 = Rs. 158.5 \). Since even the cheapest possible case costs Rs. 103.5, the variable spend can never come down to Rs. 100, so a Rs. 199 bill is never possible under option D.

Final Answer:
Only option D makes a Rs. 199 bill impossible, because its minimum possible spend of Rs. 103.5 already exceeds the required Rs. 100. \[ \boxed{\text{Option D}} \]