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Question
A sum of ₹ 500 is in the form of notes of denominations of ₹ 5 and ₹ 10. If the total number of notes is 90, find the number of notes of each type.
Solution
Let the number of ₹ 5 notes = x
∴ The number of ₹ 10 notes = 90 – x
Value of ₹ 10 notes = x × ₹ 5 = ₹ 5x
and value of ₹10 notes = (90 – x) × ₹ 10 = ₹(900 – 10x)
∴ Total value of all the notes = ₹ 500
∴ 5x + (90 – 10x) = 500
⇒ 5x + 900 – 10x = 500
⇒ -5x + 900 = 500
⇒ 900 – 500 = 5x
⇒ x = `400/5`
⇒ x = 80
∴ The number of ₹ 5 notes = x = 80
and the number of ₹ 10 notes = 90 – x
= 90 – 80 = 10
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