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
You have made wrong equations
It will be
100k +3x = 500
300k + 5x = 1100
Which will give k = 100
And hence difference 2x = rs200
500
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.
Well, let me break it down for you in a clownishly simple way!
First, let's assume that the fixed monthly rent for a telephone connection in Bangalore is 5x and in Patna is 3x (according to the given ratio).
Now, we are given two scenarios:
1. 100 calls made from a phone in Patna with a bill amount of Rs500.
2. 300 calls made from a phone in Bangalore with a bill amount of Rs1100.
Since the call rate per unit is the same in both cities, it means that the variable part of the bill (which depends on the number of calls made) should be the same.
Let's assume the variable part for both cities is y per call.
Now, for Patna, the bill is the sum of the fixed monthly rent and the variable part:
5x + (100 * y) = Rs500
Similarly, for Bangalore:
3x + (300 * y) = Rs1100
Now, solve these two equations to find the values of x and y.
Once you have those values, you can calculate the difference in the fixed monthly rent of both cities by subtracting the value of x for Patna from the value of x for Bangalore.
And voila! You've got your answer, my friend.
To find the difference in the fixed monthly rent of a telephone connection in Bangalore and one in Patna, we can use the given information and solve step by step.
Let's assign variables to the unknown values.
Let the fixed monthly rent in Bangalore be B, and in Patna be P.
According to the given information:
The ratio of the fixed monthly rent in Bangalore to Patna is 5:3.
This can be written as B/P = 5/3. ---(Equation 1)
The bill amounts corresponding to 100 calls in Patna and 300 calls in Bangalore are Rs500 and Rs1100, respectively.
So, for Patna, the variable part of the bill (call charges) is 500 - P. ---(Equation 2)
And for Bangalore, the variable part of the bill (call charges) is 1100 - B. ---(Equation 3)
Given that the call rate per unit is the same in both cities, we can equate the variable parts of the bills:
500 - P = 1100 - B. ---(Equation 4)
Now, we have a system of equations consisting of Equations 1 and 4. We can solve this system to find the values of B and P.
Multiplying Equation 1 by 3, we get:
3B = 5P. ---(Equation 5)
Substituting Equation 5 into Equation 4, we get:
500 - P = 1100 - (3B/5).
Simplifying further:
(5P - P) = 1100 - 3B.
4P = 1100 - 3B.
4P + 3B = 1100. ---(Equation 6)
Now, we have a system of equations consisting of Equations 5 and 6. We can solve this system to find the values of B and P.
By solving these equations, we find that P = 275 and B = 275 * (5/3) = 458.33 (approx).
The difference in the fixed monthly rent between Bangalore and Patna is:
B - P = 458.33 - 275 = 183.33.
Therefore, the difference in the fixed monthly rent of a telephone connection in Bangalore and Patna is approximately Rs183.33.
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