Question

If only 10 notes are needed to pay 3710 rupees , Which notes and ho many each ? *​

Answer 1

I need to pay 107 rupees using notes of 50 rupees, 10 rupees, and 1 rupee. In how many ways can I hypothetically make the payment?

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Let's say we have denote the no.of notes of Rs.50 as F, Rs.100 as H, Rs.10 as T, and Re.1 as O.

Hence 50F+100H+10T+O=107

A cursory observation leads to:

H<= 1 ; F<=2; T<= 10; O<=107

Case 1

H=1 => 50F+10T+O=7 => O=7; T=F=0; H=1 (Combination 1)

Case 2

H=0 => 50F+10T+O= 107

Sub-Case 1

F=2 => 10T+O=7 => T=0; O=7; F=2; H=0 (Combination 2)

Sub-case 2

F=1 => 10T+O=57 => T=5,4,3,2,1,0 each will give rise to one final combination (6 combinations- H=0; F=1;)

F=0 => 10T+O=107 => T=10,9,...,1,0 will give rise to 10 possible combinations (10 combinations- H=0; F=0)

Hence overall 1+1+6+10=18 combinations or 18 ways to make the payment