My friend Charles works in a post office and he sells stamps. One day a man walked in and slamming seventy five rupees on the counter requested,
"Please give me some 2 rupees stamps, six times as many one rupee stamps, and for the rest of the amount make up some 5 rupee
stamps."
Charles thought for a few moments and finally she handed over the exact fulfilment of the order to the man.
How did he do it and how many stamps of each type did he give to the man ?
Let the respective number of 2 rupee stamps and 5 rupee stamps be x and y.
Then, by the problem, # 1 rupee stamps must be 6x.
Accordingly, we must have:
2*x + 1*(6x) *5*y=75
=> 8x+5y=75
= > 8x=5(15-y) ....(#)
In other words, rhs of # is divisible by 5.
Since gcd(5,8)=1, this is only feasible if x is a multiple of 5, that is, x=5,10,15,.....
However, if x>=10, then from (#), we obtain:
5(15-y)>=80
=> 75-y=80
=> y -<= -5, which is a contradiction.
Accordingly , the only possible value of x is 5, which gives:
5(15- y)=8*5, from (#)
=> 15-y=8
=> y=7
Consequently, , Charles gave 5 two rupee stamps, 30 one rupee stamps and 7 five rupees stamps to the customer.
Edited on December 24, 2021, 6:40 pm
Puzzle Solution
