Suppose you have sufficient amount of rupee currency in three denominations

Numbers

Suppose you have sufficient amount of rupee currency in three denominations: Rs. 1, Rs. 10 and Rs. 50. In how many different ways can you pay a bill of Rs. 107?

  1. 16
  2. 17
  3. 18
  4. 19

Answer

Let the number of currency in denominations of Rs. 1, Rs. 10 and Rs. 50 be x, y and z respectively.

So, x + 10y + 50z = 107

Now, the possible values of z could be 0, 1 and 2.

For z = 0: x + 10y = 107

In this case, y can range from 0 to 10, so total 11 ways.

For z = 1: x + 10y = 57

In this case, y can range from 0 to 5, so total 6 ways.

For z = 2: x + 10y = 7

In this case, y can take only 1 value i.e 0. that means there is only 1 way.

Total number of ways = 11 + 6 + 1 = 18

The correct option is C.