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?

Puzzle – Financial institution Cashier Mistake

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 x {dollars}, then the x {dollars} grow to be x cents, and equally, 
• If initially, we had y cents, then y cents grow to be y {dollars}. Now, subsequently, since 1 greenback = 100 cents,  y {dollars} = 100 * y cents. So, now after visiting the financial institution, we had, 100*y +x (cents).

Answer half 1

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.

Answer half 2

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 by discovering the worth of y which is lower than 100 [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.