# Thread: what was the amount for the checque?

1. ## what was the amount for the checque?

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  Reply With Quote

2. ## Re: what was the amount for the checque?

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  Reply With Quote

3. ## Re: what was the amount for the checque?

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  Reply With Quote

4. ## Re: what was the amount for the checque?

I would suggest dont copy paste the answer!! Even if you do make sure you dont get caught...Who is Ms . Smith?  Reply With Quote

5. ## Re: what was the amount for the checque?

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

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suresh  Reply With Quote

6. ## Re: what was the amount for the checque?

caught red-handed  Reply With Quote

7. ## Re: what was the amount for the checque?

on top of that he was buying fruits n not newspaper  Reply With Quote

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