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प्रश्न
Form the pair of linear equations for the following problem and find their solution by substitution method.
The coach of a cricket team buys 7 bats and 6 balls for ₹ 3800. Later, she buys 3 bats and 5 balls for ₹ 1750. Find the cost of each bat and each ball.
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
उत्तर
Let the cost of one bat be x rupees
And the cost of one ball is Rs y.
Situation I
7 bats + 6 balls = 3800
⇒ 7x + 6y = 3800 ...(i)
Situation II
3 bats + 5 balls = 1750
⇒ 3x + 5y = 1750 ...(ii)
From equation (ii)
3x + 5y = 1750
⇒ 3x = 1750 – 5y
⇒ x = `(1750 - 5y)/3`
Now on putting this value of x in equation (i)
7x + 6y = 3800
⇒ `7((1750 - 5y)/3) + 6y = 3800`
⇒ 12250 – 35y + 18y = 11400
⇒ 12250 – 17y = 11400
⇒ 17y = 12250 – 11400
⇒ 17y = 850
⇒ y = `850/17`
⇒ y = 50
Now putting y = 50 in equation (ii)
⇒ x = `(1750 - 5y)/3`
⇒ x = `(1750 - 5 xx 50)/3`
⇒ x = `(1750 - 250)/3`
⇒ x = `1500/3`
⇒ x = 500
⇒ x = 500 and y = 50
Hence, the cost of one bat is Rs 500 and the cost of one ball is Rs 50.
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