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### Interesting Maths Puzzle

Interesting Maths Puzzle - 2 July

A women walks into a bank to cash out her check.
By mistake the bank teller gives her rupee amount in change, and her paise amount in rupees.
On the way home she spends 5 paise, and then suddenly she notices that she has twice the amount of her check.

How much was her check amount ?

1. 31.63 was her check amount.

2. initial check amount = 100x+y(taking units as paise)

amount she got = 100+x

eq: 100y+x = 2(100x+y) +5
so,
98y-199x = 5
condition is 0> x,y> 100

holds true only for x=63 and y = 31

3. 98y = 199x + 5

y = (199x + 5)/98 = 2x + (3x + 5)/98

Since x and y are whole numbers, so must be (3x + 5)/98.

Call it z = (3x+5)/98
so 98z = 3x + 5, or 3x = 98z - 5 or x = (98z - 5)/3

or x = 32z-1 + (2z-2)/3.

Since everything is a whole number, so must be (2z-2)/3.

Call it w = (2z-2)/3, so 3w = 2z-2 so z = (3w+2)/2 or
z = w + 1 + w/2. So w/2 must be whole, or w must be even.

So try w = 2. Then z = 4. Then x = 129. Then y = 262.

These answers are no good, but looking at the original equation,
if you decrease y by 199 and x by 98, the answer will still
obviously work, so do that:

y = 63 and x = 31.

Original check: \$31.63 Recieved: \$63.31.

Subtract a nickel: \$63.26 = 2 times \$31.63.