How a Mathematician Tricked a Rich Man with a Clever Calculation – Can You Spot the Flaw?

Dear friends,

Apply your brain like this mathematician...

Long ago, a mathematician used to cheat people. Once he borrowed Rs. 4000/- from a rich man. After a few days, he borrowed Rs. 2000/- from the same man. Many days passed, and the mathematician did not return the money to the rich man. The rich man went to the mathematician and asked for the money back. To his great surprise, the mathematician replied that there was no need to pay the debt.

"See here, friend," said the mathematician, "the sum of 4000 and 2000 is equal to zero, so I do not have any balance to pay."

The rich man took the matter to court. When the judge learned of this, he was astonished. He asked the mathematician to prove that the sum of 4000 and 2000 is zero, not 6000. The clever mathematician agreed and presented his argument:

Let a = 4000, b = 2000, and c = 6000.

a + b = c

Multiply both sides by a + b:

(a + b) (a + b) = c (a + b)

a * a + ab + ba + b * b = ca + cb

a * a + ab - ca = cb - b * b - ba

a (a + b - c) = -b (b + a - c)

So, a = -b

a + b = 0

Hence, 4000 + 2000 = 0.

Thank you and regards,

Sidheshwar :P

Ha ha, nice one. I think I got the catch.

He divided both sides by a+b-c, which is equal to zero, and division by zero is not allowed in mathematics :D

Here is one more:
a = b
a.a = a.b
a.a - b.b = a.b - b.b
(a-b)(a+b) = b(a-b)
a+b = b
Since a = b
Therefore, 2a = a
or, 2 = 1

Hi,

Hahaha! Another idea...

Since ( a + b = b ) as per sskarla:
[
a + b - b = b - b
]
[
a + 0 = 0
]
[
a = 0
]

This means the mathematician had not taken a loan of Rs. 4000.00.

Regards,
Sidheshwar

Dear friends,

Both of you are making valid points. In both cases, what you are canceling out, being equal on both sides, is actually a zero, i.e., a+b-c in the first case and b-a in the second. The cancellation of both of these terms results in 0 divided by 0. This scenario is not conceivable in mathematics.

Anyhow, it's a fun deviation from mathematics. I really enjoyed the discussion.

Regards,
Dr. Manisha

Hi, friends. You are reminding me of my scary maths teacher Suzy Thomas, from whom I used to get my daily installment of scolding because my answers in the homework I somewhat did myself never used to match the real ones. Those equations, permutations, and geometry still give me a scare when I remember those days. I felt like the dumbest student in the class. Maths really has not been my cup of tea or coffee, but thanks for posting whether I understand it or not.