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

Sue's percentage profit on each tin of green paint she sells is approximately 44.94%. This is calculated by finding the total cost of inputs, subtracting from the total sales revenue, and then finding the profit ratio to the cost.

Step-by-step explanation:

To calculate Sue's percentage profit on each tin of green paint she sells, we need to first determine the cost of producing the green paint and then subtract that cost from the selling price. The green paint is produced in a ratio of 1:4 yellow to blue paint, making 50 litres total. Therefore, Sue uses 10 litres of yellow paint and 40 litres of blue paint to make 50 litres of green paint.

Yellow paint costs £38 for a 5-litre tin, so two tins are needed (costing £76 total) to get the required 10 litres. Blue paint costs £58 for a 10-litre tin, so four tins are needed (costing £232 total) to get 40 litres. This brings the total cost to £308 for 50 litres of green paint.

Sue sells her green paint at £89.32 per 10-litre tin. Therefore, for 50 litres, she gets 5 tins x £89.32 = £446.60.

The profit Sue makes is the selling price minus the cost price, which is £446.60 - £308 = £138.60. To find the percentage profit per tin, divide the profit by the cost and multiply by 100:

(£138.60 / £308) x 100 = 44.94%

Therefore, Sue's percentage profit on each tin of green paint she sells is approximately 44.94%.

Answer 2

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 = (1)/(4) * 50 = 10 \: litres`

To determine the litres of blue paint, we say:

`blue \: paint = (4)/(5) * 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 \: \% = (selling \: price - cost \: price)/(cost \: price) * (100)/(1)`

`profit \: \% = (446.60 - 308)/(308) * (100)/(1)`

`profit \: \% = (138.60)/(308) * (100)/(1)`

`profit \: \% = 0.45 * 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 = (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%