Careful check

Logic Level 2

A man went into a bank to cash a check. In handing over the money the cashier, by mistake, gave him dollars for cents and cents for dollars. He pocketed the money without examining it, and spent a nickel on his way home. He then found that he possessed exactly twice the amount of the check. He had no money in his pocket before going to the bank. What was the exact amount of that check?


The answer is 31.63.

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

2 solutions

The amount must have been $31.63. He received $63.31. After he had spent a nickel there would remain the sum of $63.26, which is twice the amount of the check.

Jewel Jose
Sep 9, 2017

I have actually posted the same question a while back and this is my solution:

The check was for dollars 31.63.

The bank teller gave her dollars 63.31 She spent .05, and then she had dollars 63.26, which is twice the check.

Let x be the dollars of the check, and y be the cent.

The check was for 100x + y cent He was given 100y + x cent

Also 100y + x - 5 = 2(100x + y) Expanding this out and rearranging, we find: 98y = 199x + 5

or 199x ≡ -5 (mod 98) or 982x + 3x ≡ -5 (mod 98) 3x ≡ -5 ≡ 93 (mod 98) this quickly leads to x = 31

Are you really 14 years?

Syed Hamza Khalid - 3 years, 9 months ago

Log in to reply

yeah, I'm nearly 15 now!

Jewel Jose - 3 years, 9 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...