A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha

Question

A lending library has a fixed charge for the first three days and an additional charge for each day thereafter. Saritha paid ₹27 for a book kept for seven days, while Susy paid ₹21 for the book she kept for five days. Find the fixed charge and the charge for each extra day.

Accepted Answer

Let the fixed charge for the first 3 days = ₹$x$
Let the additional charge per day after 3 days = ₹$y$ Saritha's Case:
She kept the book for 7 days (3 fixed days + 4 extra days).
Total amount paid = ₹27 $$x + 4y = 27 \quad 	ext{--- (1)}$$ Susy's Case:
She kept the book for 5 days (3 fixed days + 2 extra days).
Total amount paid = ₹21 $$x + 2y = 21 \quad 	ext{--- (2)}$$ Solving equations (1) and (2):
Subtract equation (2) from equation (1): $$(x + 4y) - (x + 2y) = 27 - 21$$ $$2y = 6$$ $$y = 3$$ 
Substitute $y = 3$ into equation (2): $$x + 2(3) = 21$$ $$x + 6 = 21$$ $$x = 21 - 6$$ $$x = 15$$ Final Answer: The fixed charge for the first three days is ₹15 and the charge for each extra day is ₹3.

Pair of Linear Equations in Two Variables

❓ Sibling Questions in this Chapter