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.

Explanation

Let the fixed charged for first two days = Rs x
Let the additional charges per day after 2 days = Rs y
Latika paid Rs. 22 for six days. (Given)
2 days fixed charges + (6 - 2) days charges = 22
implies x + 4y = 22 …(1)
Anand paid Rs. 16 for books kept for four days.
2 days fixed charges + (4 - 2) days additional charges = 16
implies x + 2y = 16 ...(2)
x + 2y = 16 [from (2)]
`{:(" x + 4y = 22 [from (1)]"),( " "ul "- - -"),(" -2y = - 6 [subtracting equation (1) from (2)]"):}`
implies y = Rs. 3 per day
Now, x + 2y = 16 [from (2)]
implies x + 2(3) = 16
implies x = 16 - 6 implies x = 10
`{:("So, the fixed charges for first 2 days = Rs. 10"),("The additional charges per day after 2 days = Rs. 3 per day "):}}`