Peter and Albert shared some pens in the ratio of 5 : 7. After both each gave away 27 pens to their cousin, the ratio of the number of pens Peter had to the total number of pens left was 1 : 3. How many pens did the two boys have at first?

	Peter	Albert	Difference
Before	5x1 = 5 u	7x1 = 7 u	2x1 = 2 u
Change	- 27	- 27
After	1x2 = 2 u	2x2 = 4 u	1x2 = 2 u

Number of pens that Peter and Albert each gave to their cousin is the same.

The difference in the number of pens at first and in the end between Peter and Albert remains unchanged.  Make the difference in the number of pens the same.  LCM of 2 and 1 is 2.

Number of pens that Peter gave to their cousin
= 5 u - 2 u
= 3 u

3 u = 27

1 u = 27 ÷ 3 = 9

Number of pens that the two boys had at first
= 5 u + 7 u
= 12 u
= 12 x 9
= 108

Answer(s): 108