# Puzzle – Financial institution Cashier Mistake

You went to a financial institution to money your examine. The financial institution clerk by accident offers you: The greenback quantity is in **cents**, and the Cent quantity is in **{dollars}**. You spend 5 cents on the way in which dwelling, and then you definately understand you’ve twice the quantity of your cheque. What was the precise quantity that was written on the cheque?

**Answer:**

**Word**: *1 Greenback incorporates 100 cents.*

Let’s assume the variety of {dollars} is x and the variety of cents is y within the cheque earlier than visiting the financial institution. If 1 greenback is the same as 100 cents**, **then x {dollars} can be equal to **[100*x cents]. **Due to this fact, the entire sum of money earlier than visiting the financial institution is **[100*x + y (cents)].**

After having cashed your examine, it’s on condition that the financial institution clerk exchanges the models of cash**,** however the sum of money stays the identical. Due to this fact, on observing,

- If initially, we had
- If initially, we had
**.**So, now after visiting the financial institution, we had,**100*y +x (cents).**

Now it’s talked about that from this sum of money, you** **spent 5 cents from it, and after spending it the cash left turns into** **equal to twice the quantity** **initially, you had in examine earlier than visiting the financial institution i.e., **100*x +y cents.**

So, we’ve,

x + 100*y – 5 = 2*(100*x + y) –Quantity taken from the cashier – 5 cents which you spend whereas going dwelling is the same as twice the sum of money you had in your examine earlier than going to the financial institution.

**Simplifying the above equation: **

x+ 100*y -5 = 200*x + 2*y,or,199*x+5=98*y,or,(199*x+5)/98=y

Since** **y is the quantity in cents** **so it **can’t exceed 99** as a result of in the true world if cents exceed 99 then it may be thought-about that the entire quantity might have some variety of {dollars} and a few variety of cents,** **however we had assumed y to be purely in cents so this may increasingly contradict our assumption.

Allow us to assume we’ve 143 cents which is bigger than 99. Now we all know that 1 greenback=100 cents**, **subsequently, we’ve to transform it into {dollars} (the above equation must be glad).

- On changing we get 1 greenback and 43 cents
**(greenback = (whole cents)/100 (flooring division) and cents = (whole cents) %100).** - On taking additional examples we are able to see we are able to cut back our search house to [1 – 99] cents as cents will all the time lie between
**the vary of 1 and 99.**So, we attempt to apply the hit and trial technique**[Y < 100],**and fulfill the equation.

Due to this fact, taking, **x = 31**, for the above equation, we’ve,

199*(31) + 5 = 6174 and on dividing it by 98 i.e. (6174/98) we get 63 which is within the vary of [1 – 99], subsequently, is our ultimate reply.

Due to this fact, we get** **x = 31 and y = 63, by the above calculations. Due to this fact, initially, we had **31 {dollars}** and **63 cents** respectively.