Daniel, Tom and Julian had some beads. Tom had 40% more beads than Daniel. Tom had ⁴₇ of Julian's. After Daniel gave 40 beads to Tom, he had ¹₂ of what Tom had. How many more beads did Julian have than Tom in the end?

Daniel	Tom	Julian
5x4	7x4
	4x7	7x7
20	28	49

	Julian	Daniel	Tom	Total beads of  Daniel and Tom
Before	49x1 = 49 u	20x1 = 20 u	28x1 = 28 u	48x1 = 48 u
Change		- 40	+ 40
After	49 u	1x16 = 16 u	2x16 = 32 u	3x16 = 48 u

Number of beads that Tom had more than Daniel at first in percent
= 100%+ 40%
= 140%

140% = ¹⁴⁰₁₀₀ = ⁷₅

Daniel : Tom = 5 : 7

The number of beads that Tom had at first is repeated.  Make the number of beads that Tom had at first the same.  LCM of 7 and 4 is 28.

When Daniel gave 40 beads to Tom, the total number of beads that Tom and Daniel had at first and in the end remains the same.  Make the total number of beads that Tom and Daniel had the same.  LCM of 48 and 3 is 48.

Number of beads that Daniel gave to Tom
= 20 u - 16 u
= 4 u

4 u = 40

1 u = 40 ÷ 4 = 10

Number of beads that Julian had more than Tom in the end
= 49 u - 32 u
= 17 u
= 17 x 10
= 170

Answer(s): 170