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A Lending Library Has a Fixed Charge for the First Three Days and an Additional Charge for Each Day Thereafter. Saritha Paid Rs 27 for a Book Kept for Seven Days, While Susy Paid Rs 21 for the Book She Kept for Five Days. Find the Fixed Charge and the Charge for Each Extra Day. - Mathematics

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

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Let the fixed charge for first three days and each day charge thereafter be Rs x and Rs y respectively.

According to the question,

x + 4y = 27 ....(1)

x + 2y = 21 ....(2)

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

2y  = 6

y = 3

Subtracting the value of y in equation (1), we obtain

x + 12 = 27

x = 15

Hence, the fixed charge is Rs 15 and the charge per day is Rs 3

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
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RD Sharma Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.6 | Q 10 | Page 79
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