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Question
Form the pair of linear equation in the following problem, and find its solution (if they exist) by the elimination method:
Meena went to a bank to withdraw ₹ 2000. She asked the cashier to give her ₹ 50 and ₹ 100 notes only. Meena got 25 notes in all. Find how many notes of ₹ 50 and ₹ 100 she received.
Solution
Let the number of ₹ 50 notes = x
The number of 100 rupees notes = y
According to the condition,
Total number of notes 25
x + y = 25 ...(1)
50x + 100y = 2000
x + 2y = 40 ...(2)
Subtracting equation (1) from (2), we get
x + 2y - x - y
y = 40 - 25
y = 15
Putting y = 15 in (1),
x + 15 = 25
x = 25 - 15
x = 10
Thus, x = 10 and y = 15
∴ Number of 50 rupees notes = 10 and number of 100 rupees notes = 15
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