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Pair of Linear Equations in Two Variables
CH03 Question Bank
CBSE_CH03_QUESTION_BANK
Grade 10
Question:
[Case Study]
A 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.
(a) Let the fixed charge for 3 days be ₹$x$ and additional charge per day be ₹$y$. Form linear equations for Saritha and Susy. [1 Mark] (b) Find the additional charge per day ($y$). [1 Mark] (c) Find the fixed charge for the first 3 days ($x$). [1 Mark] (d) Find the total amount paid by a student who keeps the book for 6 days. [1 Mark]
Step-by-Step Solution
Key Concept: Case study on linear equations in two variables.
(a) Let the fixed charge for 3 days be ₹$x$ and additional charge per day be ₹$y$. Form linear equations for Saritha and Susy. [1 Mark] $x + 4y = 27$ and $x + 2y = 21$. [1.0 Mark]
(b) Find the additional charge per day ($y$). [1 Mark] $(x+4y) - (x+2y) = 27 - 21 \Rightarrow 2y = 6 \Rightarrow y = 3$. Additional charge = ₹$3$/day. [1.0 Mark]
(c) Find the fixed charge for the first 3 days ($x$). [1 Mark] $x + 6 = 21 \Rightarrow x = 15$. Fixed charge = ₹$15$. [1.0 Mark]
(d) Find the total amount paid by a student who keeps the book for 6 days. [1 Mark] $ ext{Total} = 15 + 3(3) = 15 + 9 = ₹24$. [1.0 Mark]