Same pattern as Overlapping shapes — find A : B : C. New numbers, new story. Try each one on paper, then check the working below — or watch it drawn out, the same way the problem above is.
Question 1
Three tarpaulins P, Q and R are spread out on a warehouse floor and overlap one another. The combined area of Q and R is 3/4 of the area of P. Where P overlaps Q, the overlapping part is 1/4 of Q's area. Where P overlaps R, the overlapping part is 1/2 of R's area. Altogether, the shaded (overlapping) part of P makes up 1/3 of P's area. Find P : Q : R.
Work it out on paper, then check below. ▶ See the working
Question 2
Three circular flowerbeds X, Y and Z in a park overlap one another. The combined area of Y and Z is 3/5 of the area of X. Where X overlaps Y, the overlapping part is 1/2 of Y's area. Where X overlaps Z, the overlapping part is 1/4 of Z's area. Altogether, the shaded (overlapping) part of X makes up 1/5 of X's area. Find X : Y : Z.
Work it out on paper, then check below. ▶ See the working