Respuesta :
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:
[tex]yellow \: paint = \frac{1}{4} \times 50 = 10 \: litres[/tex]
To determine the litres of blue paint, we say:
[tex]blue \: paint = \frac{4}{5} \times 50 = 40 \: litres[/tex]
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
[tex]profit \: \% = \frac{selling \: price - cost \: price}{cost \: price} \times \frac{100}{1} [/tex]
[tex]profit \: \% = \frac{446.60 - 308}{308} \times \frac{100}{1} [/tex]
[tex]profit \: \% = \frac{138.60}{308} \times \frac{100}{1} [/tex]
[tex]profit \: \% = 0.45 \times 100[/tex]
[tex]profit \: \% = 45\%[/tex]
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:
[tex]profit \: \% \: on \: each \: green \: tin = \frac{45}{5} = 9\%[/tex]
Hence, Sue's percentage profit for selling each tin of green paint is 9%.
Proof
9% × 5 tins of green paint = 45%
The percentage of profit that Sue earn on each tin of green paint she sells is 9%
How to find the percentage from the total value?
Suppose the value of which a thing is expressed in percentage is "a'
Suppose the percent that considered thing is of "a" is b%
Then since percent shows per 100 (since cent means 100), thus we will first divide the whole part in 100 parts and then we multiply it with b so that we collect b items per 100 items(that is exactly what b per cent means).
Thus, that thing in number is
[tex]\dfrac{a}{100} \times b[/tex]
For this condition,we're given that:
- Total 50 liters of green paint is made from 1:4 mixture of yellow and blue paint.
- Yellow paint is sold in 5 litres tin and each tin is of £38
- Blue paint is sold in 10 litres tin and each tin is of £58
- Selling price of 50 litres green paint in 10 litre tins is £89.32 per tin
Let yellow paint was x liters, then blue paint was 4x litres ( as their ratio must make 1:4)
Now, we have:
x + 4x = 50
5x = 50
x = 10 litres.
Thus, there was 10 litres of yellow paint, and 40 litres of blue paint.
10 litres of yellow paint = 2 tins of 5 litres of yellow paint.
Since 1 yellow paint tin costs £38
Thus, 2 yellow paint tin costs £76
40 litres of blue paint = 4 tins of 10 litres of blue paint.
Since 1 blue paint tin costs £58
Thus, 4 blue paint tin costs £232
Total cost price for making 50 litres green paint = £76 + £232 = £308
50 litres green paint = 5 tins of 10 litre green paint.
1 tin of green paint sells for £89.32
5 tins would sell for £446.6
Total profit = net selling price - net cost price = £446.6 - £308 = £138.6
Percentage of profit is counted on cost price.
Let it be p% of the cost price.
Then, we get:
[tex]\dfrac{308}{100} \times p = 138.6\\\\ p = \dfrac{138.6}{3.08} = 45[/tex]
As the percentage of profit that Sue earn was for 5 tins of green paint she sells is 45%, so for each tin, she earned 45/5 = 9% profit.
Thus, the percentage of profit that Sue earn on each tin of green paint she sells is 9%
Learn more about percent here:
https://brainly.com/question/11549320
