David had 25% more pencils than Isaac. John had 50% fewer pencils than David. David and Isaac gave John some pencils in the ratio of 3 : 4. As a result, John had 60% more pencils than before. Given that John had 48 more pencils than Isaac in the end, how many pencils did David give to John?

David	Isaac	John
5x2	4x2
2x5		1x5
10	8	5

100% + 25% = 125%
125% = ¹²⁵₁₀₀ = ⁵₄

David : Isaac = 5 : 4

100% - 50% = 50%
50% = ⁵⁰₁₀₀ = ¹₂

David : John = 2 : 1

The number of pencils that David had at first is repeated. Make the number of pencils that David had at first the same.  LCM of 5 and 2 is 10.

	David	Isaac	John
Before	10x7 =  70 u	8x7 = 56 u	5x7 = 35 u
Change			+ 3x7 = + 21 u
Comparing the changes in the number of pencils	- 3x3 = - 9 u	- 4x3 = - 12 u	+ 7x3 = + 21 u
After	61 u	44 u	8x7 = 56 u

60% x 5 
= ⁶⁰₁₀₀ x 5 
= 3 

The total number of pencils that David and Isaac gave to John is repeated.  Make the total number of pencils that David and Isaac gave to John the same.  LCM of 7 and 3 is 21.

Number of pencils that John had more than Isaac 
= 56 u - 44 u
= 12 u

12 u = 48

1 u = 48 ÷ 12 = 4

Number of pencils that David gave to John
= 9 u
= 9 x 4
= 36

Answer(s): 36