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Worked Solutions – Test 10 2021-02-05T14:14:10+00:00

## Worked Solutions – Test 10

#### Question 1

The company making the most profit generated how much money?

A: £10,223,664

B: £19,889,912

C: £26,354,165

D: £35,201,628

#### Written Solutions

The quickest way to work out this question is to work out how much profit each company makes per car.

Company A sell each car for £33,416, having spent £23,768 purchasing it and investing a further £3226. Therefore, their profit per car is $£33,416 - £23,768 - £3225 = £6423$

Therefore in total they would have generated $£6423 \times 2312 \text{ cars sold} = £14,849,976$

Company B sell each car for £33,162, having spent £24,678 purchasing it and investing a further £3006. Therefore, their profit per car is $£33,162 - £24,678 - £3006 = £5478$

Therefore in total they would have generated $£5478 \times 6426 \text{ cars sold} = £35,201,628$

Company C sell each car for £31,267, having spent £23,967 purchasing it and investing a further £2942. Therefore, their profit per car is $£31,267 - £23,967 - £2942 = £4358$

Therefore in total they would have generated $£4358 \times 4564 \text{ cars sold} = £19,889,912$

Company D sell each car for £13,095, having spent £8923 purchasing it and investing a further £1025. Therefore, their profit per car is $£13,095 - £8923 - £1025 = £3147$

Therefore in total they would have generated $£3147 \times 2011 \text{ cars sold} = £6,328,617$

Therefore the company generating the most money is company B which made £35,201,628

#### Question 2

Which company made the greatest percentage profit?

A: Company A

B: Company B

C: Company C

D: Company D

#### Written Solutions

For this question, the percentage profit is the same whether we calculate it per car or per the total number of cars sold. Our answers from question 1 will also help us calculate this answer efficiently.

Company A pay £25,668 for a car and the profit they make is $£33,416 - £23,768 - £3225 = £6423$

As a percentage profit, this would be the profit as a percentage of what they paid for each car, so can be calculated as follows:

$£6423 \div £25,668 \times 100 = 25.02\% \text{ profit}$

Company B pay £24,678 for a car and the profit they make is $£33,162 - £24,678 - £3006 = £5478$

The percentage profit would therefore be:

$£5478 \div £24,678 \times 100 = 22.17\%$

Company C pay £23,967 for a car and the profit they make is $£31,267 - £23,967 - £2942 = £4358$

The percentage profit would therefore be:

$£4358 \div £23,967 \times 100 = 18.18\%$

Company D pay £8923 for a car and the profit they make is $£13,095 - £8923 - £1025 = £3147$

The percentage profit would therefore be:

$£3147 \div £8923 \times 100 = 35.27\%$

Therefore Company D made the greatest percentage profit.

#### Question 3

To the nearest whole number, what percentage of the combined total profit was generated by company B?

A: 32%

B: 46%

C: 49%

D: 52%

#### Written Solutions

We can use answers from the previous question(s) to speed things up here. Otherwise to calculate the total profit for each company, we need to do the following calculations:

The total profit of Company A was $(£33,416 - £3226 - £25,768) \times 2312 = £10,223,664$

The total profit of Company B was $(£33,162 - £3006 - £24,678) \times 6426 = £35,201,628$

The total profit of Company C was $(£31,267 - £2942 - £23,967) \times 4564 = £19,889,912$

The total profit of Company D was $(£13,095 - £1025 - £8923) \times 2011 = £6,328,617$

The total profit of all four companies combined was:

$£10,223,664 + £35,201,628 + £19,889,912 + £6,328,617 = £71,643,821$

Therefore, Company B’s percentage of the total profit share is:

$£35,201,628 \div £71,643,821 \times 100 = 49.13\%$ or $49\%$ to the nearest whole number

#### Question 4

Next year, company D plan to sell 12% more cars and reduce their average maintenance costs per car by 15%.  Approximately how much profit will they make if their average purchase and sales prices remain the same?

A: £7.4 million

B: £7.8 million

C: £8.2 million

D: £8.9 million

#### Written Solutions

If Company D sell 12% more cars in the following year, then the number of cars they produce the following year can be calculated as follows:

$2011 \times 1.12 = 2252.32$

If their maintenance costs reduce by 15%, then their new maintenance costs will be:

$£1025 \times 0.85 = £871.25$

The new profit per car will now be:

$£13,095 - £871.25 - £8923 = £3300.75$

Therefore the total profit they will make with these new costs is:

$£3300.75 \times 2252.32 = £7,434,345.24$ which is approximately $£7.4$ million

(It would have been fine to round the 2252.32 to 2252 since it is impossible to produce 0.32 of a car, and this would not have had an impact on the final answer.)

#### Question 5

What was the approximate percentage decrease in sales of the company which made the biggest loss in sales from 2017 – 2019?

A: 3.2%

B: 6.6%

C: 8.4%

D: 9.5%

#### Written Solutions

Brewery A went from €312 to €287 which is a loss of €15.

Brewery B went from €416 to €381 which is a loss of €35.

Brewery C went from €296 to €270 which is a loss of €26.

(There is no benefit in bothering to see these numbers as hundreds of thousands of euros since this is a question about percentages.)

Therefore Brewery B was the worst hit and its sales, as a percentage decrease, can be calculated as follows:

$\dfrac{£416-£381}{£381} \times 100 = 8.413\%$ decrease or $8.4\%$ to the given approximation.

#### Question 6

In 2020, sales improve and are on average 20% more than in 2018.  If 30% of sales are generated by Brewery A, how much is generated by Brewery B if Brewery B and C’s sales are shared in the ratio of 5 : 3?

A: €4,686,000

B: €5,497,000

C: €46,860,000

D: €53,970,000

#### Written Solutions

Sales in 2018 came to a total of $€284 + €426 + €318 = €1028$

If in 2020, sales rise by 20% from this amount, then the total sales will be:

$€1028 \times 1.2 = €1233.60$

If 30% will be generated by Brewery A, then this means that 70% will be generated between Brewery B and Brewery C combined. Sales of Brewery B and Brewery C will therefore be:

$0.7 \times €1233.60 = €863.52$

If Brewery B and C’s sales are to be shared in the ratio of $5 : 3$, then this means that $\frac{5}{8}$ of this amount will be generated by Brewery B. (We are dealing in eighths because 5 + 3 = 8.)

$\frac{5}{8} \times €863.52 = €539.70$

Remember that so far we have overlooked the fact that these figures are actually in hundreds of thousands, so we will need to multiply this final answer by 100,000:

$€539.70 \times 100,000 = €53,970,000$

#### Question 7

In 2019, 4/9 of Brewery C’s sales are made in the UK.  If the exchange rate is €1 = £0.89, what is the value of Brewery C’s sales in the UK in pounds?

A: £8.25 million

B: £10.68 million

C: £11.36 million

D: £11.42 million

#### Written Solutions

Brewery C’s sales come to €270 in 2019. If $\frac{4}{9}$ of this is made in the UK, then we can calculate exactly how much is generated in the UK:

$€270 \times \frac{4}{9} = €120$

Now we simply need to convert this into pounds:

$€120 \times £0.89 = £106.80$

Remember that we have overlooked the fact that these figures are actually in hundreds of thousands, so we will need to multiply this final answer by 100,000:

$£106.80 \times 100,000 = £10,680,000 = £10.68$ million

#### Question 8

Brewery A produces two products, Black Sheep and Archbishop.   If Archbishop represents 65% of overall sales revenue in 2019 and is sold in barrels of 260 litres, how many barrels, to the nearest ten thousand, does it produce if it sells at €0.55 per litre?

A: 120,000

B: 130,000

C: 160,000

D: 180,000

#### Written Solutions

In 2019, Brewery A’s total sales revenue is €287. If 65% of this is Black Sheep, then the exact amount of Black Sheep sales is:

$€287 \times 0.65 = €186.55$

Remember that we have overlooked the fact that these figures are actually in hundreds of thousands, so we will need to multiply this answer by 100,000:

$€186.55 \times 100,000 = €18,655,000$

If the total amount of Black Sheep sales amounts to €18,655,000 and sells for €0.55 per litre, then we can calculate the exact number of litres sold as follows:

$€18,655,000 \div €0.55 = 33,918,181.82$ litres

If each barrel contains 260 litres, then the total number of barrels produced is:

$33,918,181.82 \div 260 = 130,454.5455$ or $130,000$ to the nearest ten thousand.

#### Question 9

In which month did Company C generate approximately 29% of the revenue of the 3 companies combined?

A: September

B: October

C: November

D: December

#### Written Solutions

If you take a quick look at the available answers, you will see that calculating the percentage for August is a waste of time! It is also going to be a lot easier to ignore the fact that these figures are in tens of thousands since this is a question about percentages and proportionality.

In September, the total of all three companies combined was $£8 + £14 + £23 = £45$

Company C generated £14. As a percentage, this can be calculated as follows:

$\dfrac{£14}{£45} \times 100 = 31.1\%$

In October, the total of all three companies combined was $£12 + £16 + £25 = £53$

Company C generated £12. As a percentage, this can be calculated as follows:

$\dfrac{£12}{£53} \times 100 = 22.64\%$

In November, the total of all three companies combined was $£12 + £16 + £19 = £47$

Company C generated £16. As a percentage, this can be calculated as follows:

$\dfrac{£16}{£47} \times 100 = 34.04\%$

In December, the total of all three companies combined was $£16 + £19 + £20 = £55$

Company C generated £16. As a percentage, this can be calculated as follows:

$\dfrac{£16}{£55} \times 100 = 29.09\%$

Therefore it was in December that Company C generated approximately 29% of the revenue of the three companies combined.

#### Question 10

In the period of August to December, Company A bought £13,000 of antiques and spent a further £2,000 on restoration.  If they spent £5,000 on overheads and wages, what was Company A’s percentage profit?

A: 59.9%

B: 66.2%

C: 70.6%

D: 76.3%

#### Written Solutions

Company A’s sales from August to December was $£13 + £8 + £16 + £12 + £19 = £68$ (thousand).

Company A’s costs were $£13,000 + £2,000 + £5,000 = £20,000$

Their profit was therefore $£68,000 - £20,000 = £48,000$

Their percentage profit was therefore:

$£48,000 \div £68,000 \times 100 = 70.6\%$ to one decimal place.

#### Question 11

Combined sales of the 3 antique companies decrease from December to January by 11%.  If the sales revenue in January is generated by companies A, B and C in the ratio of 7 : 4 : 9, what is the value of sales generated by companies B and C combined?

A: £289,576

B: £307,655

C: £318,175

D: £322,869

#### Written Solutions

The total sales of the three antique companies in December was $£20 + £19 + £16 = £55$ (let’s overlook the fact that we are deal in tens of thousands for the sake of simplicity.) If this amount decreases by 11%, then the total sales for January can be calculated as follows:

$£55 \times 0.89 = £48.95$

If the sales revenue in January is generated by companies A, B and C in the ratio of $7 : 4 : 9$, this means that $\frac{7}{20}$ of £48.95 was generated by Company A and $\frac{13}{20}$ generated by Company B and Company C combined. (We are dealing with twentieths because the sum of the ration is 20.)

The value of sales generated by companies B and C combined can be calculated as follows:

$£48.95 \times \frac{13}{20} = £31.8175$

We have overlooked the fact that the figures should be in tens of thousands, so we simply need to multiply this final answer by 10,000.

$£31.8175 \times 10,000 = £318,175$

#### Question 12

As a percentage to the nearest whole number, how much more is made by Company B than Company C between August to December?

A: 36%

B: 45%

C: 59%

D: 64%

#### Written Solutions

Between August and December, Company B made $£18 + £23 + £25 + £19 + £20 = £105$.

Between August and December, Company C made $£8 + £14 + £12 + £16 + £16 = £66$.

The percentage difference between Company B and Company C can be calculated as follows:

$\dfrac{£105-£66}{£66} \times 100 = 59.09\%$ or $59\%$ to the nearest whole number.

We need to use the £66 value (the Company C value) as the denominator and not £105 since the question is asking us to compare Company B to Company C and not the other way round.

#### Question 13

What was the percentage increase, to one decimal place, in the value of Vauxhall’s market share from 2017 to 2019?

A: 16.6%

B: 28.4%

C: 49.5%

D: 52.3%

#### Written Solutions

In 2017 Vauxhall’s market share was 12% of £3.2 billion. We can work out the exact value of the market share as follows:

$0.12 \times £3.2 = £0.384 \text{ billion}$

In 2019, Vauxhall’s market share was 14% of £4.1 billion. We can work out the exact value of the market share as follows:

$0.14 \times £4.1 = £0.574 \text{ billion}$

Therefore, Vauxhall’s market share increased from £0.384 billion to £0.574 billion (in fact, for the sake of simplicity, it is probably easier to overlook the fact that these figures are billions since this is a question about percentages).

As a percentage increase, this can be calculated as follows:

$\dfrac{£0.574-£0.384}{£0.384} \times 100 = 49.47\%$ or $49.5\%$ to one decimal place.

#### Question 14

What was the mean value of Hyundai’s market share over the 3 year period to the nearest 10 million pounds?

A: £790 million

B: £840 million

C: £870 million

D: £910 million

#### Written Solutions

In 2017, Hyundai generated 24% of £3.2 billion. Hyundai therefore generated $0.24 \times £3.2 \text{ billion} = £0.768 \text{ billion}$

In 2018, Hyundai generated 26% of £3.6 billion. Hyundai therefore generated $0.26 \times £3.6 \text{ billion} = £0.936 \text{ billion}$

In 2019, Hyundai generated 22% of £4.1 billion. Hyundai therefore generated $0.22 \times £4.1 \text{ billion} = £0.902 \text{ billion}$

Therefore the mean value of Hyundai’s market share was $\dfrac{£0.768 + £0.936 + £0.902}{3} = £0.868\dot{6} \text{ billion}$ Now let’s convert this into figures:

$£0.868\dot{6} \text{ billion} \times 1,000,000,000 = £868,666,666.70$

In millions, this would be $£868,666,666.70 \div 1,000,000 = £868.\dot{6} \text{ million}$ or $£870$ million to the nearest 10 million pounds.

#### Question 15

If Mazda comprise 8% of the “Other” category, what was the value of their market share between 2017 to 2019 to the nearest million?

A: £206 million

B: £215 million

C: £245 million

D: £260 million

#### Written Solutions

The value of the ‘Other’ category in 2017 was $0.26 \times £3.2 \text{ billion} = £0.832 \text{ billion}$.

The value of the ‘Other’ category in 2018 was $0.21 \times £3.6 \text{ billion} = £0.756 \text{ billion}$.

The value of the ‘Other’ category in 2019 was $0.24 \times £4.1 \text{ billion} = £0.984 \text{ billion}$.

Therefore, the overall total of the ‘Other’ category was $£0.832 + £0.756 + £0.984 = £2.572 \text{ billion}$.

If Mazda comprise 8% of this category, then their value would be:

$0.08 \times £2.572 \text{ billion} = £0.20576 \text{ billion}$

Now let’s convert this into figures:

$£0.20576 \times 1,000,000,000 = £205,760,000$

In millions, this would be $£205,760,000 \div 1,000,000 = £205.76$ million or $£206$ million to the nearest million.

#### Question 16

The projected total market share in 2020 increases at the same rate as between 2018 to 2019.  If Vauxhall increase their percentage of the overall market share to 20%, how much more revenue will they generate to the nearest million than 2019 if successful?

A: £245 million

B: £295 million

C: £320 million

D: £360 million

#### Written Solutions

In 2018, the total market share was £3.6 billion which increased to £4.1 billion in 2019. (Since this is a question about percentages, it is easier to ignore the fact that these figures are in billions.) As a percentage increase, this can be calculated as follows:

$\dfrac{£4.1-£3.6}{£3.6} \times 100 = 13.\dot{8}\%$

If the total market share increases by the same amount from 2019 to 2020, then the total market share in 2020 will be:

$1.13\dot{8} \times £4.1 \text{ billion} = £4.669\dot{4} \text{ billion}$

If Vauxhall generate 20% of this, then in 2020 they will generate:

$£4.669\dot{4} \text{ billion} \times 0.2 = £0.933\dot{8} \text{ billion}$

In 2019, Vauxhall generated 14% of £4.1 billion, so their share was worth $0.14 \times £4.1 \text{ billion} = £0.574 \text{ billion}$

Therefore, the additional revenue they generated in 2020 was $£0.933\dot{8} \text{ billion} - £0.574 \text{ billion} = £0.359\dot{8} \text{ billion}$

Let’s convert this to figures in terms of millions of pounds:

$£0.359\dot{8} \text{ billion} \times 1,000,000,000 \div 1,000,000 = £359.\dot{8}$ million or $£360$ million to the nearest million

(The recurring digits are quite annoying, so if you go with 13.8% or 13.9% at the start, it should still be abundantly clear that the correct answer option is £360 million rather than any of the other options.)

#### Question 17

What was the difference in revenue generated by the Liverpool branch between 2018 and 2019?

A: £2,056,000

B: £2,387,000

C: £20,560,000

D: £23,870,000

#### Written Solutions

In 2018, sales of all branches totalled £186 million and the Liverpool branch was responsible for 28% of this. The sales of the Liverpool branch alone can be calculated as follows:

$£186 \text{ million} \times 0.28 = £52.08 \text{ million}$

In 2019, sales of all branches totalled £197 million and the Liverpool branch was responsible for 16% of this. The sales of the Liverpool branch alone can be calculated as follows:

$£197 \text{ million} \times 0.16 = £31.52 \text{ million}$

Therefore the difference from one year to the next was $£52.08 \text{ million} - £31.52 \text{ million} = £20.56 \text{ million.}$ In figures, this is $£20.56 \times 1,000,000 = £20,560,000$

#### Question 18

If Huntington’s Real Estate increases revenue by 8% from 2019 to 2020 and the Bristol, Birmingham and Liverpool offices generate £97.8696 million combined, how much, to the nearest million, is generated by the Manchester office if the ratio of revenue for London to Manchester is 3 : 2?

A: £32 million

B: £46 million

C: £48 million

D: £56 million

#### Written Solutions

If Huntington’s increase their 2019 sales by 8%, then in 2020 their sales will be $1.08 \times £197 \text{ million} = £212.76 \text{ million}$

If the Bristol, Birmingham and Liverpool offices generate £97.8696 million between them, then if we subtract this from the total, we can work out how much was generated by the London and Manchester offices.

$£212.76 \text{ million} - £97.8696 = £114.8904 \text{ million}$

If the revenue generated by the London and the Manchester office is in the ratio of $3 : 2$, then this means that the Manchester office generates $\frac{2}{5}$of the total. (We are dealing in fifths since the sum of the ratio is 5.)

$£114.8904 \text{ million} \times \frac{2}{5} = £45.95616$ million or $£46$ million to the nearest million.

#### Question 19

Revenue is generated through two streams, sales and lettings.  In 2019, 24% of revenue from the Liverpool branch and 32% of the London branch was from sales.  How much, to the nearest million, was generated from the two branches combined for lettings?

A: £68 million

B: £74 million

C: £76 million

D: £96 million

#### Written Solutions

In 2019, the Liverpool branch generated 16% of the £197 million total.

$0.16 \times £197 \text{ million} = £31.52 \text{ million}$

Of this amount, 24% was from lettings, so 76% was from sales. Therefore, the total amount generated from sales was:

$0.76 \times £31.52 \text{ million} = £23.9552 \text{ million}$

In 2019, the London branch generated 37% of the £197 million total.

$0.37 \times £197 \text{ million} = £72.89 \text{ million}$

Of this amount, 32% was form lettings, so 68% was from sales. Therefore the total amount generated from sales was:

$0.68 \times £72.89 \text{ million} = £49.5652 \text{ million}$

Therefore the total amount generated from both office from sales in 2019 was $£49.5652 \text{ million} + £23,9552 \text{ million} = £73.5204 \text{ million or} £74 \text{ million to the nearest million.}$

#### Question 20

The 2018 revenue was up 24% form a very poor 2017, although the total revenue generated by the London office was the same in 2017 as it was in 2019.  If the Bristol office generated £13.04 million of revenue in 2017, and Manchester, Birmingham and Liverpool’s revenue were in the ratio of 5 : 3 : 2, how much revenue was generated by the Birmingham office to the nearest million?

A: £19 million

B: £21 million

C: £25 million

D: £29 million

#### Written Solutions

If revenue was up by 24% from 2017 to 2018, then the total sales in 2017 can be calculated as follows:

$£186 \text{ million} \div 1.24 = £150 \text{ million}$

The London office generated the same revenue as in 2019. In 2019, the London office generated 37% of £197 million.

$0.37 \times £197 \text{ million} = £72.89 \text{ million}$

If the total revenue of all branches in 2017 was £150 million and the London office generated £72.89 million and the Bristol office generated £13.04 million, if we subtract these values form the total, we will be left with the combined value of the Manchester, Birmingham and Liverpool offices:

$£150 \text{ million} - £72.89 \text{ million} - £13.04 \text{ million} = £64.07 \text{ million}$

If the revenue was generated by the Manchester, Birmingham and Liverpool branches in the ratio of $5 : 3 : 2$ , then this means that the Birmingham office generated $\frac{3}{10}$ of the total (we are dealing with tenths here since $5 + 3 + 2 = 10$).

$£81.46 \text{ million} \times \frac{3}{10} = £19.221 \text{ million} = £19 \text{ million to the nearest million.}$