A Lending library has a fixed charge for the first seven days and an a

1.	A Lending library has a fixed charge for the first seven days and an additional charge for each day thereafter. Amrita paid & 65 for a book kept for twelve days, while Supriya Baid80 for the book she kept for fifteen days. What charges would one have to pay to keeponthe book for 20 days?
Answer» $\large\underline{\sf{Solution-}}$ Let assume that Fixed CHARGE for the seven DAYS be Rs x and ADDITIONAL Charge per day there after be Rs y Case :- 1 Amrita paid Rs 65 for a book kept for twelve days. It means, Charge for 7 days = Rs x and Charge for extra 5 days = Rs 5y So, Total amount paid = Rs 65 $\red{\rm :\longmapsto\:x + 5y = 65 - - - (1)}$ Case :- 2 Supriya paid Rs 80 for the book, she kept for fifteen days. It means, Charge for 7 days = Rs x and Charge for extra 8 days = Rs 8y So, Total amount paid = Rs 80 $\red{\rm :\longmapsto\:x + 8y = 80 - - - (2)}$ On Subtracting equation (1) from equation (2), we get $\rm :\longmapsto\:3y = 15$ $\rm :\longmapsto\:y = 5 - - - (3)$ On substituting the value of y in equation (1), we get $\rm :\longmapsto\:x + 5 \times 5 = 65$ $\rm :\longmapsto\:x + 25 = 65$ $\rm :\longmapsto\:x = 65 - 25$ $\rm :\longmapsto\:x = 40$ So, If book is kept for 20 days. Fixed charges for 7 days = Rs 40 Additional charge per day there after = Rs 5 So, Charges for additional 13 days = 13 × 5 = 65 Total amount paid for 20 days = 40 + 65 = Rs 105