The problem you are referring to is a classic semi-variable (partly fixed and partly variable) cost problem, where the telephone bill consists of a fixed charge plus a charge that varies with the number of calls made. Here is the general approach to solve it:
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Let the fixed part of the bill be Rs. X.
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Let the variable cost per call be Rs. Y.
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When 40 calls are made, the telephone bill is Rs. 1800. So, the equation is:
X+40Y=1800X+40Y=1800X+40Y=1800 -
When another number of calls are made in another month, the bill changes according to the calls made, and you get another equation:
X+(number_of_calls)×Y=bill_amountX+\text{(number\_of\_calls)}\times Y=\text{bill\_amount}X+(number_of_calls)×Y=bill_amount
By solving these two equations, you can find the values of X (fixed charge) and Y (variable cost per call). Once you have X and Y, you can calculate the telephone bill for any number of calls. For example, if the problem also states that in another month 50 calls led to a bill of Rs. 1950, then:
- X+40Y=1800X+40Y=1800X+40Y=1800
- X+50Y=1950X+50Y=1950X+50Y=1950
Subtracting the first from the second:
- 10Y=150 ⟹ Y=1510Y=150\implies Y=1510Y=150⟹Y=15
- Substitute Y in first equation: X+40×15=1800 ⟹ X=1800−600=1200X+40\times 15=1800\implies X=1800-600=1200X+40×15=1800⟹X=1800−600=1200
So fixed charge is Rs. 1200 and cost per call is Rs. 15. If you provide the number of calls and bills of other months, I can help you find the fixed and variable parts specifically for your case. From a very similar example I found, with this method, if the bill for 540 calls is Rs. 1800 and the bill for 620 calls is Rs. 2040, the fixed amount comes to Rs. 180 and the variable cost per call comes to Rs. 3. Then the bill for 500 calls would be Rs. 1680.
If you provide the complete details like number of calls and bill for the second month, I can solve it precisely for you.
