[administration]

Three friends were playing a game of card P,Q and R. at beginning P and Q together had 50 percent more than R and R and Q together had thrice of P. At the end of the games P and Q had three times as much as R had and P and R together had 50 percent more than Q.P gained 2000 by the end of Game.
Find the total amount with them?

[administration]

Given ,

P+Q = 1.5 R and R+Q= 3P since R+Q = 3P –> P+Q+R = 4P

Also it is given that , P1+Q1 = 3R1 and P1 + R1 = 1.5 Q1 –> P1+Q1 + R1 = 4R1

Since at the end of game P+Q+R =  P1+Q1 + R1 (as no of cards will be same )

-> 4P = 4 R1 –> P= R1

 

Alsofrom, P1+Q1 = 3R1 and P1 + R1 = 1.5 Q1 –> 3R1-P1 = (P1 +R1)/1.5

–> R1 = 5/7 P1

–> P= 5/7 P1

 

also give P1 = P+2000 –> 7/5 P- P = 2000 –> P = 2000×5/2 = 5000

Hence total amount = 4 P = 20000

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