Question

The telephone bill consists of a fixed monthly rent and a variable part that varies with the number of units of calls made per month. The monthly rents charged for a telephone connection in bangalore and patna are in the ratio 5 : 3. The bill amounts corresponding to 100 calls made from a phone in patna and 300 calls made from a phone in bangalore are respectively Rs500 and Rs1100. What is the difference in the fixed monthly rent of a telephone connection in bangalore and one in patna, if call rate per unit is same in both cities?

How to do easy way please help me

Answer 1

let the fixed rent be 5x and 3x

#1:
100k + 5x = 500
20k + x = 100

#2:
300k + 3x = 1100
100k + x = 1100/3

subtract them:
80k = 1100/3 - 100 = 800/3
k = 10/3

in #1 ----> 20(10/3) + x = 100
x = 100/3

So the difference is the fixed rates
= 5x-3x
= 2x
= 200/3

I was expecting the number of calls to be a whole number, but my answers do check out:

check:
calls in patna:
100(10/3) + 5(100/3) = 500
calls in bangalore:
300(10/3) + 3(100/3) = 1100

Answer 2

You have made wrong equations
It will be
100k +3x = 500
300k + 5x = 1100
Which will give k = 100
And hence difference 2x = rs200

Answer 3

500

Answer 4

I apologize for my mistake. You are correct.

Let the fixed monthly rent for a telephone connection in Patna be 3x, and in Bangalore be 5x.

From the given information, we have:

100k + 3x = 500 ...(1)

300k + 5x = 1100 ...(2)

where k is the cost per call unit (which is the same for both cities).

Solving equation (1) for x, we get:

3x = 500 - 100k

x = (500 - 100k)/3

Substituting the value of x in equation (2), we get:

300k + 5[(500 - 100k)/3] = 1100

900k + 2500 - 500k = 3300

400k = 800

k = 2

Substituting the value of k in equation (1), we get:

100(2) + 3x = 500

3x = 300

x = 100

Therefore, the fixed monthly rent for a telephone connection in Patna is 3x = Rs. 300, and in Bangalore is 5x = Rs. 500.

The difference in the fixed monthly rent between the two cities is 5x - 3x = Rs. 200.