P, Q, and R are each mixtures of red and white paint.
The percentage by volume of red paint in P is 30%.
The percentage by volume of red paint in Q is 20%.
The mixtures P, Q, and R are combined in the proportion 12 : 5 : 3 respectively.
If the resulting mixture contains 25% by volume of red paint, what percentage by volume of mixture R is red paint?
- A25%
- B23%
- C1313%
- D1912%
- E934%
- FIt is impossible to achieve this result.
Show the answer and worked solution
answer · C
- A25%
- B23%
- C1313%
- D1912%
- E934%
- FIt is impossible to achieve this result.
Take volumes of 12, 5 and 3, so 20 in total. Counting red paint by volume, 12 × 30 + 5 × 20 + 3r = 20 × 25 where r is the percentage of red in R. That is 360 + 100 + 3r = 500, so 3r = 40 and r = 1313. The percentages must be weighted by the volumes, not simply averaged: an unweighted average would wrongly give 25%.