Question

Ashok went to a casino to play a card game. In each round, he happened to double the amount with himself and in each round he gave Rs. x to his friend. At the end of three rounds, he has left with no money. If the amount he gave to his friend in each round Rs. 20 more than the amount he started with, find the amount that he started with
\[\begin{align}
  & \text{(A) 110} \\
 & \text{(B) 120} \\
 & \text{(C) 130} \\
 & \text{(D) 140} \\
\end{align}\]

Answer 1

Hint: First of all, let us assume the initial amount that Ashok started the first round of the game is equal to y. It was given that Ashok doubled the amount after each round. In each and every round, Ashok gave x to his friend. Ashok has no money after round 3. Now we should represent the money that Ashok is having at the end of round 3 terms of x and y. Assume this as equation (1). We were also given the amount he gave to his friend in each round Rs. 20 more than the amount he started with. Let us represent this statement in terms of x and y. Assume this as equation (2). Now by solving equation (1) and equation (2), we get the values of x and y.

Complete step-by-step answer:
Let us assume the initial amount that Ashok started the first round of the game is equal to y.
From the question, it was given that in each round he doubles the amount.
We know that Ashok has started the game equal to y.
In the first round he gave x to his friend.
So, let us assume the amount Ashok is having after the first round is equal to A.
Then we get
\[\Rightarrow \text{A=2y-x}......\text{(1)}\]
Now in the second round Ashok started with two times A and he also gave x to his friend.
So, let us assume the amount Ashok is having after the second round is equal to B.
\[\Rightarrow \text{B=2A-x}.....\text{(2)}\]
Now in the third round Ashok started with two times B and he also gave x to his friend.
So, let us assume the amount Ashok is having after the third round is equal to C.
\[\Rightarrow C\text{=2B-x}.....\text{(3)}\]
Now we will substitute equation (2) in equation (1), we get
\[\begin{align}
  & \Rightarrow B=2\left( 2y-x \right)-x \\
 & \Rightarrow B=4y-3x.....(4) \\
\end{align}\]
Now we will substitute equation (4) in equation (3), we get
\[\begin{align}
  & \Rightarrow C=2(4y-3x)-x \\
 & \Rightarrow C=8y-7x......(5) \\
\end{align}\]
We were given that after three rounds Ashok had left with no money.
\[\begin{align}
  & \Rightarrow 8y-7x=0 \\
 & \Rightarrow y=\dfrac{7}{8}x....(6) \\
\end{align}\]
From the question, it was given that the amount of money Ashok spent for the first round is equal to the sum of money spent for his friend and 20.
\[\Rightarrow x=y+20....(7)\]
Now let us substitute equation (6) in equation (7), then we get
\[\begin{align}
  & \Rightarrow x=\dfrac{7x}{8}+20 \\
 & \Rightarrow \dfrac{x}{8}=20 \\
 & \Rightarrow x=160....(8) \\
\end{align}\]
So, from equation (8) it is clear that the value of x is equal to 160.
Now we will substitute equation (8) in equation (6), then we get
\[\begin{align}
  & \Rightarrow y=\dfrac{7}{8}\left( 160 \right) \\
 & \Rightarrow y=7(20) \\
 & \Rightarrow y=140.....(9) \\
\end{align}\]
So, the amount of money Ashok started with is equal to Rs. 140.

So, the correct answer is “Option D”.

Note: Students should write the value of money in terms of x and y in a correct manner. If a small mistake is made in writing the values of A, B and C then we will get a wrong relation between x and y. This will give us the wrong value of x and wrong value of y. So, the final answer will get interrupted. Students should also be careful at the calculation part. If a small mistake is done, then the final answer may go wrong.