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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Correct answer: A
Explanation
The correct answer is option 1 i.e. 16
5he number of ₹20 notes be x and the number of ₹10 notes be y.
⇒ 20x + 10y = 390
⇒ 2x + y = 39 (Equation 1)
The new amount is ₹90 less than before. This means the new amount is:
⇒ 390 - 90 = 300
⇒ 20y + 10x = 300
⇒ 2y + x = 30 (Equation 2)
Solving for y in terms of x from Equation 1:
⇒y = 39 - 2x
⇒ 2(39 - 2x) + x = 30
⇒ 78 - 4x + x = 30
⇒ 78 - 3x = 30
⇒ 3x = 48
⇒ x = 16
Substituting ( x = 16 ) in ( y = 39 - 2x ):
⇒ y = 39 - 2(16) = 39 - 32 = 7
Thus, the number of ₹20 notes is 16 .