TTMUA Lab
TMUA 2016 · Paper 1 · Question 6 of 20

TMUA 2016 Paper 1 Question 6

Algebra and functions — Weighted mixture · solving for an unknown concentration. Try it first; the answer and a full worked solution are below.

TMUA 2016 · Paper 1Algebra and functionsWeighted mixture · solving for an unknown concentration6 options
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?

  1. A25%
  2. B23%
  3. C1313%
  4. D1912%
  5. E934%
  6. FIt is impossible to achieve this result.
Show the answer and worked solution
answer · C
  1. A25%
  2. B23%
  3. C1313%
  4. D1912%
  5. E934%
  6. 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%.