A purse has 26 coins of rupees 5 and rupees 10 and the total amount is is rupees 165 how many coins of rupees 5 and how many coins of rupees 10 are there?
Answers
Coins distinct
There are 38 individual coins. If every coin was identified as being distinct, each coin is either present or absent from the donation. He can, therefore, contribute in 2^38 ways - nearly three hundred billion ways.
Coins not distinct
If the coins of the same denomination are not distinct, but you mean how many ways are there to give a combination of coins , then there are
16 ways to give 10 rupee coins - 0,1,2….15
11 ways to give 5 rupee coins - 0, 1…10
6 ways to give 2 rupee coins 0, 1,2,…5
9 ways to give 1 rupee coins 0, 1,…8
This gives 16*11*6*9 = 9504 ways to make a donation ( including zero amount)
Amount to be given
If you mean how many different total amounts can be given, then first note that the largest amount will be when all the coins are given, which is 150+50+10+8 = 218 rupees. The smallest amount is nothing - no rupees.There can be no more than 219 different amounts.
It is easy to see or write out in full that every multiple of five up to 200 can be given using combinations of 10r and 5r coins.
So, 10r and 5r coins can take us up in intervals of 5 from 0 to 200 quite easily, without using any 1r or 2r coins. We can also attain intermediate amounts up to 200 ending in 1,2,3,4, ( or 6,7,8,9) by adding 1r and 2r coins ( eg using 1r, 2r, 1r +2r, 2*2r respectively ).
For example, 189 can be obtained using 15* 10r + 7*5r +2*2r
To confirm that 201 to 218 can be obtained, we need to realise that we have used no 1s or 2s to get to 200, and there are 18 rupees worth of 1r and 2r coins left (at least one 1r coin would be needed to get the odd values).
This means that any value from 0 to 218 rupees could be given - a total of 219 options.
Explanation:
Let the no. of rs5 coin= x
no. of Rs10 coin= 20-x
now
5x + 10(20-x)= 165
5x + 200 - 10x = 165
-5x = -35 (taking 200 to RHS)
x=7
therefore RS 5 coins =7
RS10 coins= 20-7=13