A dealer mixes three types of paints P, Q and R. Type P costs $140 per litre, type Q costs $160 per litre while type R costs $256 per litre. The dealer mixed type P and Q in the ratio 5:3 to make a brand that sells at $180 per litre.
(a) Calculate his percentage profit.
(b) The dealer made a new brand by mixing the three types of paint in the ratio P:Q = 5:3 and Q:R in the ratio 2:5. Determine the ratio P:Q:R in its simplest form.
(c) The selling price of the new brand if he has to make a 40% profit.
+128474 (a) The new paint has 8 equal parts
(5/8) is paint P and (3/8) is paint Q
So.....the profit made is 180 - (5/8)140 - (3/8)(160) = 180 - 87.5 - 60 = $32.50
% profit = profit / cost to produce = 32.50 / (87.5 + 60) ≈ .22 ≈ 22%
b) P : Q = 5 : 3 Q : R = 2 : 5
P : Q = 10 : 6 Q : R = 6 : 15
So P : Q : R = 10 : 6 : 15
c) Cost to produce one litre of the new mixture
We have 10 + 6 + 15 = 31 equal parts
P= 10/31 Q = 6/31 R = 15/31
(10/31)(140) + (6/31)( 160) + ( 15/31)( 256) = $200
For a 40% profit it needs to sell at
Profit / Cost to Produce = .40
Profit / 200 = .40
Profit = 200 * .40 = 80
200 + 80 = $280
+237 (a) P:5x Q:3x (P = Q = 5x : 3x = 5:3)
per profit = (180 (5x + 3x) - 140 (5x) - 160 (3x))/(140 (5x) + 160 (3x)) * 100%
= (1440x - 1180x)/1180x * 100%
= 0.220 * 100%
= 22% or 22.03%
(b) P:Q = 5:3
P = 10x, Q = 6x (P:Q = 10x : 6x = 5:3)
Q = R = 2:5
Q = 6x, R = 5(3)x = 15x
(Q : R = 6x : 15 = 6:15 = 2:5)
=> P = Q : R = 10x = 6x = 15x = 10 : 6 : 15
(c) selling price = y
40% = (y (10x + 6x + 15x) - 140 (10x) - 160 (6x) - 256 (15x))/(140 (10x) + 160 (6x) + 256 (15x))
=> 0.4 = (31 * y / 6200x)/6200x
0.4 = (31y - 6200)/6200 => 31y = 8680, y = $280 per litre
