Wednesday, November 04, 2009

Jim bought some chocolates and gave half of it to Ken. Ken bought some sweets and gave half of it to Jim. Jim ate 12 sweets and Ken ate 18 chocolates. The ratio of Jim’s sweets to chocolates became 1:7 and the ratio of Ken’s sweets to chocolates became 1:4. How many sweets did Ken buy?

Let 2X be the no. of chocolate that Jim bought at first.

Let 2Y be the no. of sweets that Ken bought at first.

(Y – 12) / X = 1 / 7

Y / (X – 18) = 1 / 4

7Y – 84 = X ------ (1)

4Y = X – 18 ------ (2)

From (2): X = 4Y + 18

Sub (2) into (1): 7Y – 84 = 4Y + 18

3Y = 102

Y = 34

2Y = 68

Therefore the numbers of sweets that Ken buy is 68.