Puzzle | How a lot cash did the person have earlier than getting into the financial institution?

Downside Assertion :

Suppose a person had some quantity in his pockets, he is aware of a financial institution that doubles the cash instantly however the price on the entrance of the financial institution is Rs 1000 and Rs 1000 because the exit price. The person visited 3 branches of the identical financial institution and when he left the final financial institution he had Rs 0 in his pockets. Discover out what was the preliminary quantity?

Resolution:

Let’s begin from the tip:

Step1: If he doesn’t go to the third financial institution then the cash left with him: 

He gave 1000 rupees as exit price on the third financial institution, so take 1000 rupees again so quantity turns into 1000 and contained in the financial institution, it can turn into half so 500 rupees now and take the getting into price additionally so, the quantity turns into 1500 earlier than going to the third department of the financial institution.

Step2: If he doesn’t go to the second financial institution then the cash left with him:

He gave 1000 rupees as exit price on the second financial institution so, take 1000 rupees again so quantity turns into 2500 and contained in the financial institution, it can turn into half so 1250 rupees now and in addition take the entry price of 1000 rupees. so, the quantity turns into 2250 earlier than going to the second department financial institution.

Step3:  If he doesn’t go to the primary financial institution then the cash left with him:

He gave 1000 rupees as exit price on the second financial institution so, take 1000 rupees again so quantity turns into 3250 and contained in the financial institution, it can turn into half so 1625 rupees now take the entry price of 1000 rupees. so, the quantity turns into 2625 earlier than going to the primary department financial institution.

Therefore he had 2625 rupees earlier than visiting the financial institution.

Mathematical Strategy:

Let’s take the preliminary quantity he has as x:

On the first financial institution:

• Subtract 1000 rupees because the entry price so the quantity turns into (x – 1000)
• Now, this quantity turns into double contained in the again. so, the brand new quantity turns into 2*(x – 1000)
• Subtract 1000 rupees because the exit price. so, the quantity turns into 2*(x – 1000) – 1000
• Lastly, the quantity after visiting the primary financial institution is (2*x – 3000)

On the second financial institution:

• Subtract 1000 rupees as entry price so quantity turns into (2*x – 3000) – 1000 = (2*x – 4000)
• Now, this quantity turns into double contained in the again. so, the brand new quantity turns into 2*( 2*x – 4000)
• Subtract 1000 rupees because the exit price. so, the quantity turns into 2*(2*x – 4000) – 1000
• Quantity after visiting the second financial institution is (4*x – 9000)

On the third financial institution:

• Subtract 1000 rupees as entry price so quantity turns into (4*x – 9000) – 1000 = (4*x – 10000)
• Now, this quantity turns into double contained in the again. so, the brand new quantity turns into 2×(4*x – 10000)
• Subtract 1000 rupees because the exit price. so, the quantity turns into 2×(4*x – 10000) – 1000
• Quantity after visiting a 3rd financial institution is (8*x – 21000)

It’s on condition that he had 0 rupees left after popping out from the third financial institution:

so,  8*x – 21000 = 0
       8*x = 21000
       x = 21000 / 8
       x = 2625

Subsequently, Initially, he had 2625 rupees in his pockets.