The figure, not drawn to scale, is made up of 3 different triangles Q, R and S. 15% of triangle Q and 35% of triangle S is shaded. The shaded area of Q is the same as the shaded area of S. What fraction of the figure is shaded if 20% of Triangle R is shaded?

Unshaded area of Q	Shaded area of Q	Unshaded area of S	Shaded area of S
17x7	3x7	13x3	7x3
119 u	21 u	39 u	21 u

15% = ¹⁵₁₀₀ = ³₂₀
35% = ³⁵₁₀₀ = ⁷₂₀
20% = ²⁰₁₀₀ = ¹₅
The shaded area of Q is the same as the shaded area of S.

Make the LCM of the shaded area of Q and shaded area of S the same.
LCM of 3 and 7 = 21

¹₅ of R is shaded
= Shaded area of Q + Shaded area of S
= 21 u + 21 u
= 42 u

Fraction of R that is unshaded 
= 1 - ¹₅
= ⁴₅ 

¹₅ of R = 42 u
⁴₅ of R = 4 x 42 u = 168 u

Fraction of the figure that is shaded if 20% of Triangle R is shaded
= ^{42 + 42}_{119 + 168 + 39 + 42 + 42}
= ⁸⁴₄₁₀
= ⁴²₂₀₅

Answer(s): ⁴²₂₀₅