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 was left with no money. If the amount he gave to his friend in each round was Rs. $20$ more than the amount he started with, find the amount (in Rs. ) that he started with

• A. $110$
• B. $120$
• C. $130$
• D. $140$

Answer 1

Answer: (D)

$140$

Let, Amount of money Ashok started with $=Rs.y$

Amount of money left after 1st round$=Rs.(2y-x)$

Amont of money left after 2nd round $=2(2y-x)-x=4y-3x$

Amount of money left after 3rd round $=Rs.2(4y-3x)-x$

A.T.Q,

$2(4y-3x)-x=0$

$⟹8y-6x-x=0$

$⟹8y-7x=0$

$⟹y=\frac{7x}{8}$ ---------(i)

$x=y+20$ --------(ii)

$⟹x=\frac{7x}{8}+20$ -------from(i)

$⟹x=\frac{7x+160}{8}$

$⟹8x-7x=160$

$⟹x=160$

$\therefore y=140$ -------from (ii)

$\therefore$ Ashok started with $Rs.140$