## Mathematical reasoning and mathematics, are they same? If not, which one is more difficult?

My friend told me the story and asked me the questions. This is just a recount.

### The problem

This is an incident that happened many years ago.

One day Bhabababu, a fairly wealthy man, decided to test the world-worthiness of his young grandson and asked him, “Khokon, can you get this cheque cashed in my bank? You know where it is. Last month I took you with me.”

Khokon was a smart young lad full of enthusiasm. He said proudly, “Yes Dadu, of course.”

So he took the cheque from his Dadu, went to bank, and confidently cashed the cheque.

At home when he handed over the money to his Dadu, Bhabababu counted the money twice. He couldn’t believe it. With deep surprise mixed with a tinge of anxiety he asked, “Khokon, what did you do with the money?”

Khokon replied apprehensively, “Why Dadu, I have spent only 20 paise from the money I got from the Bank as tram fare. Did I do anything wrong?” His Dadu replied, “No Khokon, you didn’t. The cashier did.”

Being keen on mathematical puzzles, he understood the mystery.

Continuing, he instructed Khokon, “The money that I got is exactly double of what I wrote in the cheque. By mistake the cashier had given you the rupees written as paise and paise written as rupees in my cheque. Here, take this extra money. I have added 40 paise for your two-way tram fare. Go quick Khokon. The cashier might be in trouble!”

**Two questions:**

- What was the cheque amount, and how did you get the answer?
- Can you deduce it mathematically, meaning, can you produce a deduction that is full of equations and mathematical procedures?

**Information:** 100 paise made 1 rupee.

For my part, I can say, I will publish in this space, names and other details of any puzzler who sends the** acceptable answers to both the questions** by the time **I publish my answers.** The answers to be mailed to puzzleanswers@suresolv.com.

At least one week's time you have. That should be enough if you are interested.

**Source of the puzzle:** Unknown.

### Solution:

Solution given in detailed session, * Reverse cheque puzzle solution*.

### Puzzles you may enjoy

#### Mathematical puzzles

**Reverse cheque puzzle**

**Reverse cheque puzzle solution**

**Counting eggs puzzles based on Euclid's division lemma**

#### Logic analysis puzzles

**Method based solution to Einstein's logic analysis puzzle, whose fish**

**How to solve Einstein's puzzle whose fish confidently, improved method based solution**

#### Matchstick puzzles

**Solution to 6 triangles to 5 triangles in 2 moves, first matchstick puzzle**

**Matchstick puzzle 5 squares to 4 squares in 2 moves**