Question

There r 36 coins of 25 Paise 10 Paise 5 Paise of rs 3
Find no.of 25 Paise coins

Answer 1

Let there be m of 25p coins, and p number of 5paise.
  Then there are n = 36 - m - p number of 10p coins.
  Assume that there is at least 1 of each type of coin.

Their total value in paise is :
       25 m + 10 n + 5 p = 300 paise
        25 m + 10 (36 - m - p) + 5 p = 300
             5 p = 15 m + 60 

     p = 3 m + 12

As   m >= 1,    p >= 15  and  p is a multiple of 3.   m , n , p are all integers.

    m = 1       p = 15      n = 36 - 15 - 1 = 20
    m = 2       p = 18      n = 16
    m = 3         p = 21     n = 12
    m = 4        p = 24      n = 8
     m = 5        p = 27     n = 4

  So there are five combinations of coins possible.