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

Rather than solving an inequality, plug each option's SMS count into both billing formulas and compare the two totals directly.

1. 38 local SMS a month: old bill is $38 \times 1.5 = 57$, new bill is $38 \times 0.6 + 35 = 22.8+35 = 57.8$. The new bill is higher, so this person does not benefit.
2. 40 local SMS a month: old bill is $40 \times 1.5 = 60$, new bill is $40 \times 0.6+35 = 24+35=59$. The new bill is lower, so this person benefits.
3. 60 local SMS a month: old bill is $60 \times 1.5=90$, new bill is $60 \times 0.6+35=36+35=71$. The new bill is lower, so this person benefits too.
4. 59 local SMS a month: old bill is $59 \times 1.5=88.5$, new bill is $59 \times 0.6+35=35.4+35=70.4$. The new bill is lower here as well, so this person benefits.

Only the 38 SMS case shows the new scheme costing more, 57.8 against 57, so this is the one person who should stick with the old plan.

Let's summarize:

• Compare $1.5x$ against $0.6x+35$ for each count.
• Every option above 38 SMS gives a lower new scheme bill.
• Only 38 SMS a month leaves the customer worse off under the new scheme.

So the person sending 38 SMS a month does not benefit.

\[ \boxed{\text{38 local SMS a month}} \]