Alice, Ben and Cathy shared some money. Ben's share is 1/3 of the money. 1/2 of Alice's share is 2/3 of Cathy's share. If Ben's share is $56, how much must Alice give to Cathy so that both Alice and Cathy would have the same amount of money?
1. Look for the values that is given in qn. The value given here is $56. Hence we must try to match the value to the unit.
In this qn,
Ben’s share = 1/3 of money = $56.
Hence Alice and Cathy must make up 2/3 of money = $56 x 2 = $112.
2. Relate the fractions given in qn.
Look at this statement “1/2 of Alice's share is 2/3 of Cathy's share. “
This means 1 unit of A’s share = 2 units B’s. A has 2 units in total, we have to change to B’s equal, that means A has 2x2=4 units. Hence now, A to C = 4 : 3.
Alice and Cathy = 7 units = $112.
A = 112 / 7 x 4 = $168
C = 112 / 7 x 3 = $126
Alice must give ½ the difference btw them to make same amount for both.
Hence Alice must give [168-126] / 2 = $21.
