Question

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

Answer 1

0$x + y = 90 \\ x = 90 - y \\ 5x + 10y = 500 \\ 5(90 - y) + 10 = 500 \\ 450 + 5y + 10 = 500 \\ 460 + 5y - = 500 \\ 5y = 500 - 460 \\ 5y = 40 \\ y = 8 \: \: \: \: (1) \\ x + y = 90 \\ x + 8 = 90 \\ x = 90 - 8 \\ x = 82 \: \: \: \: \: \: \: (2)$
therefore the numbers of 5 rupees notes are 82 and that of 10 rupees notes are 8.