A sum of ₹ 500 is in the form of denominations of ₹ 5 and ₹ 10. If the total number of notes is 90, find the number of notes of each type.

Let the number of ₹ 5 notes be x.

Then, the number of ₹ 10 notes = (90 - x).

Total value of ₹ 5 notes = 5x

Total value of ₹ 10 notes = 10 × (90 - x) = 900 - 10x

According to the question, the total sum is ₹ 500:

∴ 5x + (900 - 10x) = 500

⇒ 5x + 900 - 10x = 500 $\quad$ [Removing brackets]

⇒ 5x - 10x = 500 - 900 $\quad$ [Transposing +900 to RHS]

⇒ -5x = -400

⇒ x = $\dfrac{-400}{-5}$

⇒ x = 80

Number of ₹ 5 notes = x = 80.

Number of ₹ 10 notes = (90 - x) = (90 - 80) = 10.

Hence, number of ₹ 5 notes = 80 and number of ₹ 10 notes = 10.