Question

Arnab needs to pay Rs.210 for his dinner. He has an unlimited supply of Rs 2, Rs 5 and Rs 10 notes; in how many ways can he pay?

• A. 210
• B. 253
• C. 231
• D. none of these

Answer 1

The correct option is A

210

Equation become like 2x + 5y + 10z = 210, where
X should be a multiple of 5 and Y should be a multiple of 2. So, we can take X and Y as 5P and 2Q respectively.
Now equation becomes:-
10P + 10Q + 10Z = 210;
P + Q + Z = 21

where P, Q and Z are non-negative integers. Number o f solutions of the given equation is ${}^{23}{C}_2$ = 253. Option (b).