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Question

A shopkeeper gives books on rent for reading.

She takes a fixed charge for the first two days, and an additional charge for each day thereafter.

Latika paid 22for a book kept for six days, while Anand paid 16 for the book kept for four days.

Find the fixed charges and the charge for each extra day.


A

13,2

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B

10,3

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C

12,9

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D

14,5

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Solution

The correct option is B

10,3


Let the fixed charge for two days be x and the additional charge be y per day

Step 1: Form the linear equation in two variables for Latika:

Number of days for Latika =6=2+4

Charges for Latika=Fixedchargefortwodays+4×Additionalchargeperday

=x+4y

And, it is given that Latika paid 22

x+4y=22x=22-4y.......(1)

Step 2: Form the linear equation in two variables for Anand:

Number of days for Anand =4=2+2

Charge for Anand=Fixedchargefortwodays+2×Additionalchargeperday

=x+2y

And, it is given that Anand paid16

x+2y=16x=16-2y.........(2)

Step 3: Solve for x and y:

On comparing equation (1) and (2), we get,

22-4y=16-2y2y=6y=3

Substituting y=3 in equation (1), we get,

x=22-43=22-12=10

Therefore, a fixed charge for two days=10 and an additional charge=3 per day

Hence, the correct option is (B)


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