Howard, Tim and Henry had some balls. Tim had 40% more balls than Howard. Tim had ²₅ of Henry's. After Howard gave 66 balls to Tim, he had ¹₅ of what Tim had. How many more balls did Henry have than Tim in the end?

Howard	Tim	Henry
5x2	7x2
	2x7	5x7
10	14	35

	Henry	Howard	Tim	Total balls of  Howard and Tim
Before	35x1 = 35 u	10x1 = 10 u	14x1 = 14 u	24x1 = 24 u
Change		- 66	+ 66
After	35 u	1x4 = 4 u	5x4 = 20 u	6x4 = 24 u

Number of balls that Tim had more than Howard at first in percent
= 100%+ 40%
= 140%

140% = ¹⁴⁰₁₀₀ = ⁷₅

Howard : Tim = 5 : 7

The number of balls that Tim had at first is repeated.  Make the number of balls that Tim had at first the same.  LCM of 7 and 2 is 14.

When Howard gave 66 balls to Tim, the total number of balls that Tim and Howard had at first and in the end remains the same.  Make the total number of balls that Tim and Howard had the same.  LCM of 24 and 6 is 24.

Number of balls that Howard gave to Tim
= 10 u - 4 u
= 6 u

6 u = 66

1 u = 66 ÷ 6 = 11

Number of balls that Henry had more than Tim in the end
= 35 u - 20 u
= 15 u
= 15 x 11
= 165

Answer(s): 165