Question

Sue makes 50 litres of green paint by mixing litres of yellow paint and litres of blue paint in the ratio 1:4. Yellow paint is sold in 5 litre tins and each tin of yellow paint costs £38. Blue paint is sold in 10 litre tins and each tin of blue paint costs £58. Sue sells all the green paint she makes in 10 litre tins at £89.32 per tin. Work out Sue's percentage profit on each tin of green paint she sells.

Answer 1

Answer:

Sue's percentage profit = 9% on each tin of green paint she sells.

Step-by-step explanation:

Litres of green paints mixed = 50 litres

Ratio of litres of yellow paint and litres of blue paint = 1:4.

To determine the litres of yellow paint, we say:

$yellow \: paint = \frac{1}{4} \times 50 = 10 \: litres$

To determine the litres of blue paint, we say:

$blue \: paint = \frac{4}{5} \times 50 = 40 \: litres$

Since yellow paint is sold in 5 litres per tin and each tin cost £38; she has 10 litres of yellow paint in all. That implies that she has 10/5 = 2 tin of yellow paint. If one tin cost £38; 2 tin cost 2 × £38 = £76

Similarly,

Since blue paint is sold in 10 litres per tin and each tin cost £58; she has 40 litres of blue paint in all. That implies that she has 40/10 = 4 tin of blue paint. If one tin cost £58; 4 tin cost 4 × £58 = £232

Total cost of yellow and blue paints = £232 + £76

= £308

Since Sue sells all the green paint she makes in 10 litre tins at £89.32 per tin and she has 50 litres in all; we say: 50/10 litres = 5 tins = 5 × £89.32 = £446.60.

Thus, selling price of the green paint = £446.60

$profit \: \% = \frac{selling \: price - cost \: price}{cost \: price} \times \frac{100}{1}$

$profit \: \% = \frac{446.60 - 308}{308} \times \frac{100}{1}$

$profit \: \% = \frac{138.60}{308} \times \frac{100}{1}$

$profit \: \% = 0.45 \times 100$

$profit \: \% = 45\%$

Sue's percentage profit for selling all the tins of green paint is 45%, having sold 5 tins. Therefore, Sue's percentage profit for selling each of the paint will be:

$profit \: \% \: on \: each \: green \: tin = \frac{45}{5} = 9\%$

Hence, Sue's percentage profit for selling each tin of green paint is 9%.

Proof

9% × 5 tins of green paint = 45%