A has twice as much money as B. They play together, and at the end of

1.	A has twice as much money as B. They play together, and at the end of the first game, B wins one third of A's money from A ; what fraction of the sum that B now has, must A win back in the second game so that they may have exactly equal money?
Answer» ☆ CORRECT ANSWER : 1/10 ☆ Explanation : LET A has ₹ 200 at the starting of game, then B has ₹ 100 at the starting of game. After the game, money left with A = 200 - 200/3 = ₹ 400/3 ∴ Total money with B = 100 + 200/3 = ₹ 500/3 Let the FRACTION of money lost by B = N Then, 500/3 - N x 500/3 = 400/3 + N x 500/3 ⇒ 500/3 - 400/3 = 500N/3 + 500N/3 ⇒ 100/3 = 1000N/3 ∴ N = (100/3) x (3/1000) = 1/10 so, the fraction of money lost is 1/10.

A has twice as much money as B. They play together, and at the end of the first game, B wins one third of A's money from A ; what fraction of the sum that B now has, must A win back in the second game so that they may have exactly equal money?

Answer»

LET A has ₹ 200 at the starting of game, then B has ₹ 100 at the starting of game.

After the game, money left with A = 200 - 200/3 = ₹ 400/3

∴ Total money with B = 100 + 200/3 = ₹ 500/3

Let the FRACTION of money lost by B = N

Then, 500/3 - N x 500/3 = 400/3 + N x 500/3

⇒ 500/3 - 400/3 = 500N/3 + 500N/3

⇒ 100/3 = 1000N/3

∴ N = (100/3) x (3/1000) = 1/10

so, the fraction of money lost is 1/10.