Question

Can anyone show the method of following ques

There are total 36 coins with raj. Out of them there are 25 paise coin, 10 paise coin and 5paise coins.total money with raj is rs 3. Find the no. Of coins.

Answer 1

Let the total  number of coins be  N.       N = 36.

Let there be n number of 10 paise coins. Their value     n * 10  paise
let there be m number of 25 paise coins.  Their valie   m * 25 paise

So, there are (N - m - n) number of 5 paise coins.
    Their value   (N-m-n) * 5 paise  = (36 - m - n) * 5 paise = 180 - 5 m - 5 n  paise

The total value:     25 m + 10 n + 180 - 5 m - 5 n = 300 paise
           20 m + 5 n  = 120

           4 m + n = 24
      n = 60 - 4 m = 4 (6 - m)   
     Thus n is a multiple of 4.

    we also say that there is at least one 25 paise, at least one 5 paise and at least one 10 paise coin present.


1) 
    n = 4:   m = 5
    there are  4 of 10 paise, 5 of 25 paise, and  27  of 5 paise coins.

2)  n = 8 ,  m = 4
     so there are  8 of 10 paise, 4 of 25 paise, and 24 of 5 paise coins.

3)  n = 12   ,  m = 3
     so there are  12 of 10 paise,  3 of 25 paise, and 21 of 5 paise coins

4)
    n = 16 ,  m = 2
     so there are 16 of 10 paise, 2 of 25 paise coins, and 18 of 5 paise.
5)
    n = 20  m  = 1
    there are  20 of  10 paise ,  1 of 25 paise coins,  and 15 of 5 paise coins.

Answer 2

Let there be x number of 10 paise coins.
y number of 25 paise coins.
that means, the no. of 5 paise coins = (36 - x - y)
The total value:     25x + 10y + 5(36-x-y) = Rs 3
⇒ 25x + 10y + 180 - 5x - 5y = 300
           20x + 5y  = 120
           y = 24 - 4x = 4(6 - x)   
  
As y is the multiple of 4, 
a) y = 4 then x = 5
  10 paise = 4, 25 paise = 5, and  5 paise coins = 27.

b)   y = 8 ,  x = 4
  10 paise = 8, 25 paise = 4, and  5 paise coins = 24

c)  y = 12   , x = 3
10 paise = 12, 25 paise = 3, and  5 paise coins = 21

d)    y = 16 ,  x = 2
10 paise = 16, 25 paise = 2, and  5 paise coins = 18

e)    y = 20  x = 1
 There are  10 paise = 20, 25 paise = 1, and  5 paise coins = 15