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A telephone service provider charges a price of P for a new connection, and allows 30 free calls within that. On every extra call beyond the 30th one, the charge is Rs 5. Raja has 2 connections, on one of which he makes calls, and on the other, R calls, (where both and R are greater than or equal to 30) resulting in 2 bills of Rs 500 and Rs 400 respectively. Had he made all the calls on a single connection instead, his bill would have come to just Rs 800. What is the value of P?
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A telephone service provider charges a price of P for a new connection...
- **Given Information**
Given that the telephone service provider charges a price of P for a new connection and allows 30 free calls within that. On every extra call beyond the 30th one, the charge is Rs 5. Raja has 2 connections, one resulting in a bill of Rs 500 and the other resulting in a bill of Rs 400. Had he made all the calls on a single connection instead, his bill would have come to just Rs 800.
- **Calculating the number of extra calls**
Let the number of extra calls made on the first connection be x and on the second connection be R - x.
- **Calculating the total cost for each connection**
For the first connection: P + 5(x)
For the second connection: P + 5(R - x)
- **Given Bills**
According to the given information:
P + 5(x) = 500
P + 5(R - x) = 400
If all calls were made on a single connection:
P + 5(R) = 800
- **Solving the equations**
Solving the above equations will give:
P = 200
R = 100
x = 40
- **Conclusion**
Therefore, the value of P, which is the price for a new connection, is 200. This means that Raja pays Rs 200 for a new connection and Rs 5 for every extra call beyond the 30 free calls for each connection.
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A telephone service provider charges a price of P for a new connection, and allows 30 free calls within that. On every extra call beyond the 30th one, the charge is Rs 5. Raja has 2 connections, on one of which he makes calls, and on the other, R calls, (where both and R are greater than or equal to 30) resulting in 2 bills of Rs 500 and Rs 400 respectively. Had he made all the calls on a single connection instead, his bill would have come to just Rs 800. What is the value of P?
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