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 Rs 22 for a book kept for six days, while Anand paid Rs 16 for the book kept for four days. Find the fixed charges and the charge for each extra day.

Let Latika takes a fixed charge for the first two day is Rs x and additional charge for each day thereafter is Rs y.

Now by first condition.

Latika paid Rs 22 for a book kept for six days i.e., for first two days as Rs x and remaining Rs 4y.

x + 4y = 22 …(i)

and by second condition,

Anand paid Rs 16 for a book kept for four days i.e., for first two days as x’ and remaining Rs 2y.

x + 2y = 16 …(ii)

Now, subtracting Eq. (ii) from Eq. (i), we get

2y = 6

y = 3

On putting the value of y in Eq. (ii), we get

x + 2(3) = 16

x = 10

Hence, the fixed charge = Rs 10

and the charge for each extra day Rs 3.

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