Simon, Gabriel and Vaidev had some pens in the ratio of 6 : 7 : 13. Vaidev gave 40% of his pens to Simon and Gabriel. As a result, Simon had the same number of pens as Gabriel and Vaidev had 13 fewer pens than Simon.

1. What was the percentage increase in Simon's pens after receiving from Vaidev?
2. How many pens did Gabriel have at first?

Simon	Gabriel	Vaidev	Total
6 u	7 u	13 u	26 u
+ 5.2 u		- 5.2 u
9.1 u	9.1 u	7.8 u	26 u

(a)
Number of pens that Vaidev gave away
= 40% x 13
= ⁴⁰₁₀₀ x 13
= 5.2 u

Number of pens that Simon and Gabriel each had in the end
= (26 u - 7.8 u) ÷ 2
= 18.2 u ÷ 2
= 9.1 u

Increase in the number of pens that Simon had
= 9.1 u - 6 u
= 3.1 u

Percentage increase in Simon's pens after receiving from Vaidev
= ^3.1₆ x 100%
= 51.666666666667%

(b)
9.1 u = 7.8 u + 13
9.1 u - 7.8 u = 13
1.3 u = 13

1 u = 13 ÷ 1.3 = 10

Number of pens that Gabriel had at first
= 7 u
= 7 x 10
= 70

Answer(s): (a) 51.666666666667%; (b) 70