Mathematics

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

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Let for first three days charge be ₹ x and for the days after that charge be ₹ y per day.

Given,

Geeta paid ₹ 27 for a book kept for seven days.

∴ x + (7 - 3)y = 27

⇒ x + 4y = 27 ……..(1)

Mohit paid ₹ 21 for a book kept for five days.

∴ x + (5 - 3)y = 21

⇒ x + 2y = 21 ……..(2)

Subtracting equation (2) from (1), we get :

⇒ (x + 4y) - (x + 2y) = 27 - 21

⇒ x - x + 4y - 2y = 6

⇒ 2y = 6

⇒ y = $\dfrac{6}{2}$

⇒ y = ₹ 3.

Substituting value of y in equation (1), we get :

⇒ x + 4(3) = 27

⇒ x + 12 = 27

⇒ x = 27 - 12

⇒ x = ₹ 15.

Hence, fixed charge = ₹ 15 and charge for each extra day = ₹ 3.

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