Question

A new SMS scheme is introduced at 60 paise per local SMS, along with an additional fixed monthly charge of Rs. 35 (the earlier rate was Rs. 1.50 per local SMS with no fixed charge). A person sending which of the following will NOT benefit from switching to the new scheme?

• A. 38 local SMS a month
• B. 40 local SMS a month
• C. 60 local SMS a month
• D. 59 local SMS a month

Hint:

Set up the old bill as 1.5 times the SMS count and the new bill as 0.6 times the count plus Rs. 35, then see which count keeps the new bill higher.

Answer 1

The Correct Option is A

Step 1: Write the old monthly bill.
Let x be the number of local SMS sent in a month. Under the old rate, the bill is \( 1.5x \).

Step 2: Write the new monthly bill.
Under the new scheme, every SMS costs 60 paise plus a flat Rs. 35 charge, so the bill is \( 0.6x + 35 \).

Step 3: Find the breakeven point.
The new scheme only helps once it costs less than the old one, so solve \( 1.5x > 0.6x + 35 \).

Step 4: Simplify the inequality.
Subtracting \( 0.6x \) from both sides gives \( 0.9x > 35 \), so \( x > 35/0.9 \), which works out to \( x > 38.89 \) approximately.

Step 5: Apply the whole number rule.
Since messages are counted in whole numbers, the new scheme starts saving money only from 39 messages a month onward. Anyone sending 38 or fewer messages ends up paying more, or the same, under the new scheme.

Step 6: Check the given options.
38 falls below the 38.89 cutoff, so this person does not benefit, while 40, 59 and 60 all lie above the cutoff and do benefit.

Final Answer:
\[ \boxed{\text{38 local SMS a month does not benefit}} \]