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Home » Form the pair of linear equations in the following problems, and find their solutions (i) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs.27 for a book kept for seven days, while Susy paid Rs.21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
Form the pair of linear equations in the following problems, and find their solutions (i) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs.27 for a book kept for seven days, while Susy paid Rs.21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.
CBSE | Class 10 | Exercise 3.4 | Pair of Linear Equations in Two Variables
Form the pair of linear equations in the following problems, and find their solutions (i) A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid Rs.27 for a book kept for seven days, while Susy paid Rs.21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Solution:

 

Let the fixed charge for the first three days be Rs.A and the charge for each day extra be Rs.B.

 

According to the information given,

 

A\text{ }+\text{ }4B\text{ }=\text{ }27\text{ }\ldots \ldots \ldots .\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots .\text{ }\left( i \right)

 

A\text{ }+\text{ }2B\text{ }=\text{ }21\text{ }\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots ..\text{ }\left( ii \right)

 

When equation (ii) is subtracted from equation (i) we get,

 

2B\text{ }=\text{ }6

 

    \[B\text{ }=\text{ }3\text{ }\ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \left( iii \right)\]

 

Substituting B = 3 in equation (i) we get,

 

A\text{ }+\text{ }12\text{ }=\text{ }27

 

A\text{ }=\text{ }15

 

Hence, the fixed charge is Rs.15

 

And the Charge per day is Rs.3

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