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Worked Solutions – Test 3 2021-02-05T14:13:53+00:00

## Worked Solutions – Test 3

#### Question 1 Which supermarket made the greatest percentage of their revenue from alcohol sales?

A: Tesco

B: Asda

C: Morrison

D: Sainsbury

#### Written Solutions

Tesco’s total revenue was $£57 + £104 + £18 + £19 + £9 = \pounds207$ (million). Alcohol sales were $\pounds104$ (million).
The percentage of the alcohol sales was:

$104 \div 207 \times 100 = 50.24\%$

Asda’s total revenue was $£53 + £92 + £12 + £18 + £6 = \pounds181$ (million). Alcohol sales were $\pounds92$ (million).
The percentage of the alcohol sales was:

$92 \div 181 \times 100 = 50.82%\$

Morrison’s total revenue was $£44 + £84 + £15 + £21 + £7 = \pounds171$ (million). Alcohol sales were $\pounds84$ (million).

The percentage of the alcohol sales was:

$84 \div 171 \times 100 = 49.12\%$

Sainsbury’s total revenue was $£62 + £98 + £16 + £13 + £9 = \pounds198$ (million). Alcohol sales were $\pounds98$ (million). The percentage of the alcohol sales was:

$98 \div 198 \times 100 = 49.49\%$

Therefore Asda made the greatest percentage of their revenue from alcohol sales.

#### Question 2 Tesco’s revenue came from cash purchases and card payments in the ratio of 2 : 7.  How much revenue came from Amex payments if 1/7 of card payments were made by Amex?

A: £23 million

B: £26 million

C: £29 million

D: £32 million

#### Written Solutions

Tesco’s total revenue was $\pounds207$ million. If cash purchases and card payments were in the ratio of $2 : 7$, then card payments accounted for $\frac{7}{9}$ of all transactions (we are dealing with ninths because the sum of the ratio is 9).

We can now work out the value of all the card transactions:

$\pounds207$ (million) $\times \frac{7}{9} = \pounds161 ($ million

If $\frac{1}{7}$ of the $\pounds161$ million was from Amex payments, we can easily work this out:

$\pounds161$ million $\times \frac{1}{7} = \pounds23$ million

or

$\pounds161$ million $\div 7 = \pounds23$ million

#### Question 3 Morrison’s total revenue increased by 15% the following year and alcohol sales comprised 38% of annual revenue.  To the nearest million, what was the difference in sales of alcohol between 2018 and 2019?

A: £4 million

B: £8 million

C: £9 million

D: £12 million

#### Written Solutions

Morrison’s total revenue was $\pounds171$ million. If their sales increased by $15\%$, then the following year they would have made:

$1.15 \times \pounds171 \text{ million} = \pounds196.65 \text{ million}$

If alcohol comprised $38\%$ of this amount, then the value of the total alcohol sales was:

$0.38 \times \pounds196.65 \text{ million} = \pounds74.727 \text{ million}$

The previous year, Morrison’s alcohol sales came to a total of $\pounds84$ million, therefore the difference was:

$\pounds84 - \pounds74.727 = \pounds9.273 \text{ million, so} \pounds9$ million to the nearest million.

#### Question 4 Asda’s clothing sales increase by 20% in 2019 with men’s clothing and women’s clothing being sold in the ratio of 2 : 3.  If the average spend on women’s clothing in 2019 was £34.99, how many women’s clothing transactions took place in 2019 to the nearest fifty million?

A: 150 million

B: 200 million

C: 250 million

D: 300 million

#### Written Solutions

Asda’s clothing was $\pounds12$ million. If it increased by $20\%$, then the new value would be:

$\pounds12 \text{ million} \times 1.2 = \pounds14.4$ million

If men’s clothing and women’s clothing was sold in the ratio of $2 : 3$, this means that women’s clothing accounted for $\frac{3}{5}$ of the total (we are dealing in fifths because the sum of the ratio is 5). Therefore the total value of women’s clothing sales was:

$\pounds14.4$ million $\times \frac{3}{5} = \pounds8.64$ million

If the average spend was $\pounds34.99$, then the number of women’s clothing transaction can be calculated as follows:

$\pounds8.64$ million $\div \pounds34.99 = 246,927$ million

To the nearest fifty million, this would be 250,000 million transactions.

#### Question 5 In 2018, what was the value of Morrison’s market share?

A: £48,600,000

B: £584,000,000

C: £486,000,000

D: £5,840,000,000

#### Written Solutions

In 2018, the total market share was $\pounds7.3$ billion. Morrison’s accounted for $8\%$ of this, so the value of their market share can be calculated as follows:

$\pounds7.3 \text{ billion} \times 0.08 = \pounds0.584$ billion

$\pounds0.584 \text{ billion} \times 1,000,000,000 = \pounds584,000,000$

#### Question 6 What was the mean value of the market share of Sainsbury’s over the 3 year period?

A: £777,600,000

B: £865,800,050

C: £1,128,000,000

D: £1,224,000,000

#### Written Solutions

In 2017, the total market share was $\pounds6.2$ billion. Sainsbury’s market share was $16\%$, so their market share had a value of:

$\pounds6.2 \text{ billion} \times 0.16 = \pounds0.992$ billion

In 2018, the total market share was $\pounds7.3$ billion. Sainsbury’s market share was $16\%$, so their market share had a value of:

$\pounds7.3 \text{ billion}\times 0.16 = \pounds1.168$ billion

In 2019, the total market share was $\pounds6.8$ billion. Sainsbury’s market share was $18\%$, so their market share had a value of:

$\pounds6.8 \text{ billion} \times 0.18 = \pounds1.224$ billion

Therefore, the mean value of their market share was:

$\dfrac{\pounds0.992 \text{ billion} + \pounds1.168 \text{ billion} + \pounds1.224 \text{ billion}}{3} = \pounds1.128$ billion

$\pounds1.128 \text{ billion} \times 1,000,000,000 = \pounds1,128,000,000$

#### Question 7 What was the revenue of the Co-op in 2019 if it comprised ¾ of the ‘Other’ category?

A: £0.84 billion

B: £968,000,000

C: £1.02 billion

D: £1.36 billion

#### Written Solutions

In 2019, the total market share was $\pounds6.8$ billion and the ‘Other’ category accounted for $20\%$ of this. Therefore, the value of the ‘Other’ category was:

$\pounds6.8 \text{ billion} \times 0.2 = \pounds1.36$ billion

If the Co-op accounted for $\frac{3}{4}$ of this, then their market share was worth:

$1.36 \times \frac{3}{4} = \pounds1.02$ billion

#### Question 8 The projected total market share in 2020 is £7.5 billion.  Morrison’s are aiming to increase their market share to 16%.  How much more revenue will they generate compared to 2019 if they hit this target?

A: £28,000,000

B: £280,000,000

C: £384,000,000

D: £466,000,000

#### Written Solutions

In 2019, Morrison’s market share was $12\%$ of the total market share of $\pounds6.8$ billion, so their market share was worth:

$\pounds6.8 \text{ billion} \times 0.12 = \pounds0.816$ billion

If the total market share in 2020 is expected to be £7.5 billion and Morrison’s are looking to have 16% of it, then, if they succeed, their market share will be worth:

$\pounds7.5 \text{ billion} \times 0.16 = \pounds1.2$ billion

This would be a difference of:

$\pounds1.2 \text{ billion} - \pounds0.816 \text{ billion} = \pounds0.384$ billion

$0.384 \text{ billion} \times 1,000,000,000 = \pounds384,000,000$

#### Question 9 What was the difference in percentages of voter turnout over the period, assuming a voting population of 60m in 2005, that increased by 22% to 2019?

A: 2.16%

B: 3.32%

C: 4.62%

D: 5.08%

#### Written Solutions

If, in 2005, there was a population of 60 million which increased by 22% in 2019, we can calculate the population in 2019 as follows:

$60$ million $\times 1.22 = 73.2$ million

The number of people who voted in 2005 was $9 + 8 + 4 + 3 = 24$ million.

The percentage of people who voted in 2005 was:

$24$ million $\div 60$ million $\times 100 = 40\%$

The number of people who voted in 2009 was $14 + 13 + 4 + 2 = 33$ million.

The percentage of people who voted in 2009 was:

$33 \text{ million} \div 73.2 \text{ million} = 45.08\%$.

Therefore the difference in percentages is simply $45.08\% - 40\% = 5.08\%$

#### Question 10 People under 50 years of age and over 50 vote in the ratio 7:4. How many over 50 voters were there in 2019?

A: 12 million

B: 15 million

C: 18 million

D: 21 million

#### Written Solutions

The number of people who voted in 2009 was $14 + 13 + 4 + 2 = 33$ million.

Over 50 voters comprise $\frac{4}{11}$ of the voting population (we are deadline with elevenths because $7 + 4 = 11$).

Therefore we can calculate the number of over 50 voters as follows:

$33$ million $\times \frac{4}{11}$ = 12 million over 50s

#### Question 11 36% of the vote is required to form a government. In how many of the years was this passed by at least one party?

A: 1

B: 2

C: 3

D: 4

#### Written Solutions

For this question, we simply need to look at the party that received the most votes are work out whether or not this is greater than or equal to 36$\%$.

In 2005, the Conservative party received 9 million votes. In total, $9 + 8 + 4 + 3 = 24$ million votes were cast.

Therefore, the Conservative party received $9 \div 24 \times 100 = 37.5\%$ of the vote.

In 2006, the Labour party received 11 million votes. In total, $11 + 9 + 7 + 4 = 31$ million votes were cast.

Therefore, the Labour party received $11 \div 31 \times 100 = 35.48\%$ of the vote.

In 2015, the Labour party received 11 million votes. In total, $11 + 10 + 7 + 4 = 32$ million votes were cast.

Therefore, the Labour party received $11 \div 31 \times 100 = 34.375\%$ of the vote.

In 2019, the Labour party received 14 million votes. In total, $14 + 13 + 4 + 2 = 33$ million votes were cast.

Therefore, the Labour party received $14 \div 33 \times 100 = 42.42\%$ of the vote.

$36\%$ of the overall vote was gained by the winning party in 2005 and 2019, so 2 is the answer.

#### Question 12 The “Other” category comprises three other parties, A, B and C.  A and B receive votes in the ratio 1 : 2, and B and C receive votes in the ratio of 4 : 7.  To the nearest million, how many votes did party C receive in total in the four elections?

A: 6 million

B: 8 million

C: 10 million

D: 11 million

#### Written Solutions

Over the 4 elections, the ‘Other’ party received a total of $3 + 4 + 8 + 4 = 19$ million votes.

The issue we have with the ratio is that the B share is not the same in both ratios. In the ratio with A, B’s share is 2, whereas in the ratio with C, the B share is 4. We will need to adjust one of the ratios. If A and B receive votes in the ratio of $1 : 2$, this is the equivalent of receiving votes in the ratio of $2 : 4$. Now we have the same value for the B share in both ratios.

Therefore, the ratio of A : B : C is $2 : 4 : 7$. This means that party C received $\frac{7}{13}$ of all the votes (we are dealing with thirteenths because $2 + 4 + 7 = 13$).

The number of votes that party C received can be calculated as follows:

$19 \text{ million} \times \frac{7}{13} = 10.23$ million or $10$ million to the nearest million.

#### Question 13 What percentage of the overall sales of the 3 garages combined in 2019 was made from MOT revenue?  Give your answer to one decimal place.

A: 14.6%

B: 19.7%

C: 26.6%

D: 27.9%

#### Written Solutions

First of all, we need to work out how much money was generated overall by the 3 garages:

$12 + 14 + 8 + 8 + 10 + 11 + 6 + 9 + 8 + 14 + 12 + 16 = 128$ (thousand)

The total revenue generated from MOTs was:

$12 + 14 + 8 = 34$ (thousand)

As a percentage, the MOT sales accounted for $34 \div 128 \times 100 = 26.6\%$

#### Question 14 As a percentage, how much more revenue is expected to be generated in 2020 from windscreens than in 2019?  Give your answer to the nearest whole number.

A: 7%

B: 13%

C: 16%

D: 24%

#### Written Solutions

In 2019, the revenue generated from windscreens was $6 + 9 + 8 = 23$ (thousand). The projection for 2020 is 260 (hundred). This question is tricky since the top table is in thousands, whereas the bottom table is in hundreds, so we need to be careful with these figures:

$23 \text{ thousand} = 23,000$ $260 \text{ hundred} = 26,000$

The percentage increase in sales is $\dfrac{26,000 - 23,000}{23,000} \times 100 = 13.04\%$ (or $13\%$ to the nearest whole number.

#### Question 15 Garage C generated the same percentage of sales in 2019 as in 2018.  How much did garage C make to the nearest pound in 2018?

A: £29,968

B: £35,687

C: £38,297

D: £40,683

#### Written Solutions

First of all, we need to work out how much money was generated overall by the 3 garages in 2019:

$12 + 14 + 8 + 8 + 10 + 11 + 6 + 9 + 8 + 14 + 12 + 16 = \pounds128,000$

In 2019, Garage C generated $8 + 11 + 8 + 16 = \pounds43,000$

As a percentage, this is $\pounds43,000 \div \pounds128,000 \times 100 = 33.59375\%$

In 2018, the combined sales of the 3 garages was $300 + 260 + 200 + 380 = \pounds114,000$

If Garage C generated $33.59375\%$ of overall revenue, then Garage C generated $\pounds114,000 \times 0.3359375 = \pounds38,296.88$ or $\pounds38,297$ to the nearest pound.

Even if you rounded the $33.59375\%$ earlier in the question, you would probably get an answer that was pretty close to answer A, and nowhere near answers B, C and D.

#### Question 16 Revenue in 2020 increase by 3% from 2019.  By how much have the 3 garages missed the overall target for 2020?

A: £9,065

B: £12,784

C: £17,160

D: £21,865

#### Written Solutions

First of all, we need to work out how much money was generated overall by the 3 garages in 2019:

$12 + 14 + 8 + 8 + 10 + 11 + 6 + 9 + 8 + 14 + 12 + 16 = \pounds128,000$

If the revenue increases by $3\%$, then the 2020 revenue can be calculated as follows:

$\pounds128,000 \times 1.03 = \pounds131,840$

The 2020 projection was $480 + 320 + 260 + 430 = \pounds149,000$

Therefore the garages missed their projection by $\pounds149,000 - \pounds131,840 = \pounds17,160$

#### Question 17 What was the percentage decrease in profit for Spain from 2012 to 2013 if costs increased by 15% but revenue stayed the same?

A: 6.6%

B: 7.75%

C: 12.3%

D: 12.5%

#### Written Solutions

The profit for Spain was $€650 \text{ million} - €200 \text { million} = €450 \text{ million}$.

If costs increased by $15\%$ from €200 million, then the total costs for 2013 can be calculated as follows:

$€200 \times 1.15 = €230$ million

If in 2013, the costs were €230 million and the revenue remained the same, then the overall profit in 2013 was $€650 \text{ million} - €230 \text{ million} = €420$ million

If profit decreased from €450 million to €420 million, the percentage decrease can be calculated as follows:

$\dfrac {€450 - €420}{€450} \times 100 = 6.6\%$

#### Question 18 The UK has a revenue of £687 million in 2012 and has costs of €65 for every £1,000 of revenue. What is the overall profit for the UK in euros to the nearest million? (€1 is the equivalent of £0.88.)

A: €465 million

B: €524 million

C: €736 million

D: €812 million

#### Written Solutions

If the UK has costs of €65 for every $\pounds1,000$ of revenue, we need to work out how many thousands of revenue it generates.

If the UK generates$\pounds687,000,000$, this is the equivalent of 687,000 thousands of pounds, so the costs incurred would be $687,000 \times €65 = €44,655,000$.

If the UK has a revenue of $\pounds687$ million, this is the equivalent of $\pounds687,000,000 \div \pounds0.88 = €780,681,820$.

The overall profit is $€780,681,820 - €44,655,000 = €736,026,821$ or $€736$ million to the nearest million.

#### Question 19 What is the approximate difference in profit of Spain and Poland in 2014 if Spain increases its profit by 3% each year and Poland increases its profit by 12% each year?

A: €46 million

B: €101 million

C: €376 million

D: €477 million

#### Written Solutions

Spain’s profit in 2012 is $€650 - €200 = €450$ million.

Poland’s profit in 2012 is $€450 -€150 = €300$ million.

If Spain increases its profit by $3\%$ over the following two years, then in 2014 the profit it generates can be calculated as follows:

$€450 \text{ million} \times1.03 \times 1.03 = €477.405$ million

If Poland increases its profit by $12\%$ over the following two years, then in 2014 the profit it generates can be calculated as follows:

$€300 \text{ million} \times 1.12 \times 1.12 = €376.32$ million

Therefore the difference between the profit of the two countries in 2014 is $€477.405 - €376.32 = €101.085$ million or $€101$ million euros to the nearest million.

#### Question 20 Which country’s profit is the highest as a proportion of its revenue in 2012?

A: Spain

B: France

C: Germany

D: Poland

#### Written Solutions

Spain’s revenue is 650 million. Spain’s profit is $€350 - €200 = €450$ million.

As a proportion of revenue, Spain’s profit is $€450 \div €650 \times 100 = 69.23\%.$

France’s revenue is 1100 million. France’s profit is $€1100 - €500 = €600$ million.

As a proportion of revenue, France’s profit is $€600 \div €1100 \times 100 = 54.54\%.$

Germany’s revenue is 1050 million. Germany’s profit is $€1050 - €350 = €700$ million.

As a proportion of revenue, Germany’s profit is $€700 \div €1050 \times 100 = 66.6\%.$

Poland’s revenue is 450 million. Poland’s profit is $€450 - €150 = €300$ million.

As a proportion of revenue, Poland’s profit is $€300 \div €450 \times 100 = 66.6\%.$

Therefore, Spain has the biggest profit as a proportion of its revenue.