Aman has certain number of notes of denomination ₹20 and ₹10 which amount to ₹390. If the numbers of notes of each kind are interchanged, then the new amount is ₹90 less than before. Find the number of notes of ₹20 denomination.

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Accepted Answer

Let the number of ₹20 notes be x and the number of ₹10 notes be y.

Given:
20x + 10y = 390  ----(1)

When the numbers of notes are interchanged, the amount becomes:
20y + 10x = 390 - 90 = 300  ----(2)

From (1): 20x + 10y = 390
From (2): 20y + 10x = 300

Multiply (2) by 2:
40y + 20x = 600

Subtract (1) from this:
(40y + 20x) - (20x + 10y) = 600 - 390
40y + 20x - 20x - 10y = 210
30y = 210
y = 7

Substitute y = 7 into (1):
20x + 10*7 = 390
20x + 70 = 390
20x = 320
x = 16

Therefore, the number of ₹20 notes is 16.

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