NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 2(v)

NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 2(v)

Question:

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :

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.

Given:

Saritha paid Rs 27 for a book kept for 7 days.
Susy paid Rs 21 for a book kept for 5 days.
Fixed charge for first 3 days and additional charge for each day thereafter.

To Find:

Fixed charge and charge for each extra day.

Formula:

Elimination method for solving linear equations.

Solution:

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

For Saritha: x + 4y = 27 ---(1)

For Susy: x + 2y = 21 ---(2)

Subtracting equation (2) from equation (1):
(x + 4y) - (x + 2y) = 27 - 21 ⇒ 2y = 6 ⇒ y = 3

Substituting y = 3 in equation (2): x + 2(3) = 21 ⇒ x + 6 = 21 ⇒ x = 15

Result:

Fixed charge = Rs 15
Charge for each extra day = Rs 3

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