Question

A total of 90 currency notes, consisting only of ₹ 5 and ₹ 10 denominations, amount to ₹ 500. Find the number of notes in each denomination.

Answer 1

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