a man started to play a card game .in the first round he doubled the amount and he gave away a certain amount say P to his friend.In the second round,he tripled the amount left with him after the first round and gavew away an amount 2P to his friends.in the third round he quadrupled the amount left with him after the second round and gave away an amount P to his friend and was finally left with no money.if he gave away a total of RS.160 to his friend,then what was the money left with him?

Question

a man started to play a card game .in the first round he doubled the amount and he gave away a certain amount say P to his friend.In the second round,he tripled the amount left with him after the first round and gavew away an amount 2P to his friends.in the third round he quadrupled the amount left with him after the second round and gave away an amount P to his friend and was finally left with no money.if he gave away a total of RS.160 to his friend,then what was the money left with him?

Answer 1

let the amount he started with be x

after first round he has 2x-P

in 2nd round he tripled that and gave away 2P
so has left
6x - 3P - 2P = 6x - 5P

in 3rd round he quadrupled the amount and gave away P
so he has left
24x - 20P - P = 24x - 21P

amount given away = P + 2P + P = 160
P = 40

but at the end he has nothing left, so
24x - 21P = 0
24x - 21(40) = 0
x = 35

He started with RS 35

check:
in first round: doubled , gave away P
70-40 = 30
in 2nd round: tripled, gave away 2P
90 - 80 = 10
in 3rd round: quadrupled , gave away P
40 - 40 = 0

my solution checks out.

Answer 2

To find the amount of money the man initially had, we can use a backward calculation. Let's start with the money he had left after the final round.

Let M be the amount left with the man after the third round.

In the third round, he quadrupled the amount (M) and gave away P to his friend. This means he had 4M + P before giving away P, so he had 3M left.

In the second round, he tripled the amount (3M) and gave away 2P to his friend. This means he had 3 * 3M - 2P left.

In the first round, he doubled the amount (9M - 2P) and gave away P to his friend. This means he had 2 * (9M - 2P) - P = 18M - 5P left.

Since he finally had no money left, we can write the equation: 18M - 5P = 0.

We also know that he gave away a total of RS.160 to his friend: P + 2P + P = 160.

Combining the two equations, we have: P = 160 / 4 = 40.

Substituting this value of P back into the first equation: 18M - 5 * 40 = 0.

Simplifying, we get: 18M - 200 = 0.

Adding 200 to both sides gives us: 18M = 200.

Now, we can solve for M: M = 200 / 18 = 11.11 (approximately).

Therefore, the money left with the man after the third round is approximately RS.11.11.