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प्रश्न
A total of 90 currency notes, consisting only of ₹ 5 and ₹ 10 denominations, amount to ₹ 500. Find the number of notes in each denomination.
उत्तर
Let the number of ₹ 5 notes be ‘x’
And number of ₹ 10 notes be ‘y’
Total numbers of notes is x + y = 90 ...(given)
The total value of the notes is 500 rupees.
Value of one ₹ 5 rupee note is 5
Value of x ₹ 5 rupee notes is 5 × x = 5x
∴ Value of y ₹ 10 rupee notes is 10 × y = 10y
∴ The total value is 5x + 10y which is 500
∴ we have 2 equations:
x + y = 90 ...(1)
5x + 10y = 500 ...(2)
Multiplying both sides of (1) by 5, we get
5 × x + 5 × y = 90 × 5
5x + 5y = 450
Subtracting (3) from (2), we get
5x + 10y = 500
(−) (−) (−)
5x + 5y = 450
0 + 5y = 50
∴ y = `50/5` = 10
Substitute y = 10 in equation (1)
x + y = 90
⇒ x + 10 = 90
⇒ x = 90 – 10
⇒ x = 80
There are ₹ 5 denominations are 80 numbers and ₹ 10 denominations are 10 numbers
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