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How many different sums of money can be formed from the four type of notes Rs 10, Rs 20, Rs 50 and Rs 100 ?

Question

How many different sums of money can be formed from the four type of notes Rs 10, Rs 20, Rs 50 and Rs 100 ?

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Solution

The question is asking how many different sums of money can be formed using four types of notes: Rs 10, Rs 20, Rs 50, and Rs 100.

To answer this question, we need to consider that each type of note can be used any number of times, including not at all.

  1. If we don't use any note, there is only 1 way (which is Rs 0).
  2. If we use only Rs 10 notes, we can form any multiple of 10, so there are infinite ways.
  3. If we use only Rs 20 notes, we can form any multiple of 20, so there are infinite ways.
  4. If we use only Rs 50 notes, we can form any multiple of 50, so there are infinite ways.
  5. If we use only Rs 100 notes, we can form any multiple of 100, so there are infinite ways.

Now, if we start combining the notes:

  1. If we combine Rs 10 and Rs 20 notes, we can form any multiple of 10, so there are infinite ways.
  2. If we combine Rs 10 and Rs 50 notes, we can form any multiple of 10, so there are infinite ways.
  3. If we combine Rs 10 and Rs 100 notes, we can form any multiple of 10, so there are infinite ways.
  4. If we combine Rs 20 and Rs 50 notes, we can form any multiple of 10, so there are infinite ways.
  5. If we combine Rs 20 and Rs 100 notes, we can form any multiple of 20, so there are infinite ways.
  6. If we combine Rs 50 and Rs 100 notes, we can form any multiple of 50, so there are infinite ways.

And if we combine all three or all four types of notes, we can form any multiple of 10, so there are infinite ways.

So, the answer is that there are infinite ways to form different sums of money using these four types of notes.

This problem has been solved

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