Japheth, Billy and Ahmad had a total of 62 pens. The ratio of Billy's pens to Ahmad's pens was 2 : 3 at first. Japheth and Billy each gave away ¹₂ of their pens. Given that the three boys had 43 pens left, how many pens did Japheth have in the end?

	Japheth	Billy	Ahmad	Total
Comparing Billy and Ahmad at first		2 u	3 u
Before	2 p	2x1 = 2 u	3 u	62
Change	- 1 p	-1x1 = - 1 u		- 19
After	1 p	1x1 = 1 u	3 u	43

Total number of pens that Japheth and Billy gave away
= 62 - 43
= 19

The number of pens that Billy had at first is repeated.  Make the number of pens that Billy had at first the same.  LCM of 2 and 2 is 2.

1 p + 1 u = 62 - 43
1 p + 1 u = 19
1 p = 19 - 1 u --- (1)

1 p + 1 u + 3 u = 43
1 p + 4 u = 43
1 p = 43 - 4 u --- (2)

(1) = (2)
19 - 1 u = 43 - 4 u
4 u - 1 u = 43 - 19
4 u - 1 u = 24
3 u = 24

1 u = 24 ÷ 3 = 8

Substitute 1 u = 8 into (1).
1 p = 19 - 1 u
1 p = 19 - 1 x 8
1 p = 19 - 8

1 p = 11

Number of pens that Japheth had in the end
= 1 p
= 11

Answer(s): 11