Mr. Jhon went bank to collect cash for his cheque. The bank teller mistakenly given him dollars instead of cents and cents instead of dollars. After buying a fruits for 50 cents, he noticed that he had left exactly three times as much as the original cheque. what was original cheque amount?

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suresh

Suppose original cheque has x dollar and y cents
bank teller gave him y dollars and x cents
after spending 50 cents he is left with 100y + x - 50
which is equal to 3[100x + y]

hence 100y + x - 50 = 3[100x + y]
which results into 97y - 299x = 50

the solution to this equation is x = 18 and y = 56;
Hence original cheque amount was 18 dollar and 56 cents

__________________
[B][COLOR="Blue"]Anyone who thinks he knows all the answers, must not be up-to-date on the questions[/COLOR][/B]
[B]Anshul[/B]:)

Good answer smart....

Here is my way of solution....

Solution by Simultaneous Equations
Let x be the number of dollars in the check, and y be the number of cents. Consider the numbers of dollars and cents Ms Smith holds at various times. The original check is for x dollars and y cents. The bank teller gave her y dollars and x cents. After buying the newspaper she has y dollars and x - 50 cents. We are also told that after buying the newspaper she has three times the amount of the original check; that is, 3x dollars and 3y cents.

Clearly (y dollars plus x - 50 cents) equals (3x dollars plus 3y cents). Then, bearing in mind that x and y must both be less than 100 (for the teller's error to make sense), we equate dollars and cents.

As -50 (x - 50) 49 and 0 3y 297, there is a relatively small number of ways in which we can equate dollars and cents. (If there were many different ways, this whole approach would not be viable.) Clearly, 3y - (x - 50) must be divisible by 100. Further, by the above inequalities, -49 3y - (x - 50) 347, giving us four multiples of 100 to check.

If 3y - (x - 50) = 0, then we must have 3x = y, giving x = -25/4, y = -75/4
If 3y - (x - 50) = 100, then (to balance) we must have 3x - y = -1, giving x = 47/8, y = 149/8
If 3y - (x - 50) = 200, then we must have 3x - y = -2, giving x = 18, y = 56
If 3y - (x - 50) = 300, then we must have 3x - y = -3, giving x = 241/8, y = 747/8
There is only one integer solution; so the check was for $18.56.

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suresh

I would suggest dont copy paste the answer!! Even if you do make sure you dont get caught...Who is Ms . Smith?
Dere is mention of some Mr. John in your question who is absent in your answer!!

__________________
[B][COLOR="Blue"]Anyone who thinks he knows all the answers, must not be up-to-date on the questions[/COLOR][/B]
[B]Anshul[/B]:)

I assure it's not happen again...Thanks.

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suresh

caught red-handed

on top of that he was buying fruits n not newspaper