NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.2 Question 3(iii)
NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.2 Question 3(iii)
Question:
Form the pair of linear equations for the following problems and find their solution by substitution method.
The coach of a cricket team buys 7 bats and 6 balls for Rs 3800. Later, she buys 3 bats and 5 balls for Rs 1750. Find the cost of each bat and each ball.
Given:
Cost of 7 bats and 6 balls = Rs 3800
Cost of 3 bats and 5 balls = Rs 1750
To Find:
Cost of each bat and each ball
Formula:
Substitution method
Solution:
Let the cost of each bat be x and the cost of each ball be y.
From the given information, we can form the following equations:
7x + 6y = 3800 ---(1)
3x + 5y = 1750 ---(2)
From equation (2), we can express x in terms of y:
3x = 1750 - 5y ⇒ x = 1750 - 5y 3
Substitute this value of x into equation (1):
7( 1750 - 5y 3 ) + 6y = 3800
Solving for y:
8750 - 35y 3 + 6y = 3800 ⇒ 8750 - 35y + 18y = 11400 ⇒ -17y = 2650 ⇒ y = 50
Substitute the value of y back into the expression for x:
x = 1750 - 5(50) 3 = 1750 - 250 3 = 1500 3 = 500
Result:
Cost of each bat = Rs 500
Cost of each ball = Rs 50
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