skamal7 wrote:

A chess player won 25 percent of the first 20 games he played and all of his remaining games. What is the ratio of the number of games he won to the number of the games he lost?

(1) If the player had won 25 percent of the total games he played, he would have lost 30 more games than he actually did.

(2) The player won 75 percent of the games he played.

I approached the problem in this way,

Let x be the number of games played after the first 20 games. Now we already know, that out of the 20 games, 5 were won by the player and 15 lost.

Also, that since he doesnt loose any more games, the total number of losses remain to be 15.

But the games won can be assumed as 5 + x

Hence the desired ratio is 5+x:15

To calculate value of x we use the given statements:

Stamement 1. if the player had won 25% of the total games i.e. games lost = 75/100(20 + x) = 15 + 3/4x.

=> 15+3/4x -15 = 30

=> 3/4x = 30

=> x = 4/3 * 30 = 40.

Hence the ratio can be found as 45:15.

For Statement 2. If the player had won 75 of total games i.e. 5+x/20+x = 75/100 => x = 40

Hence the ratio is again found to be 45:15

The answer for me would be [D]**edited..typo! , both the statments are individually sufficient.

Regards,

Arpan

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