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Worked Solutions – Test 2 2021-02-05T14:13:51+00:00

## Worked Solutions – Test 2

#### Question 1 In 2016, the total market share was £1.8 million which rose on average by £0.35 million year on year.  What was the difference between Vodacom’s market share between 2016 and 2019?

A: £90,000

B: £120,000

C: £570,000

D: £450,000

#### Written Solutions

In 2016 the value of Vodacom’s market share was 25% of £1.8 million. Therefore, in 2016, Vodacom’s market share was worth

$\pounds1.8$ million $\times 0.25 = \pounds0.45$ million

If the overall market share increased by $\pounds0.35$ million every year, then we need to calculate the value of the total market share in 2019:

$\pounds1.8$ million $+ \pounds0.35$ million$+ \pounds0.35$ million + $\pounds0.35$ million $= \pounds2.85$ million

If the total market share was worth $\pounds2.85$ million in 2019, then the value of the Vodacom market share was

$\pounds2.85 \times 0.2 = \pounds0.57$ million

Therefore the difference in value of the Vodacom share was $\pounds0.57$ million$- \pounds0.45$ million$= \pounds0.12$ million$= \pounds120,000$

#### Question 2 Fone Factory’s figures for 2019 were investigated by the Inland Revenue and found to be incorrect.  Their market share was in fact 45% and not 35% as stated.  If their 35% market share represented a value of £0.9975 million, what was the value of their 45% market share?

A: £775,833

B: £1,097,250

C: £1,282,500

D: £1,185,000

#### Written Solutions

If the figure of $35\%$ represents an amount of $\pounds0.9975$ million, then the easiest way to calculate $45\%$ is to work out $1\%$ first.

If $35\%$ = $\pounds0.9975$ million,

then

$1\%$ = $\pounds0.9975$ million $\div 35 = \pounds0.0285$ million.

If $1\%$ = $\pounds0.0285$ million

then

$45\%$ = $\pounds0.0285$ million $\times 45 = \pounds1.2825$ million or $\pounds1,282,500.$

#### Question 3 Vodacom had an improved market share in 2020 of 27% which was worth £0.999 million.  What was the value of the combined market share?

A: £1,613,700

B: £3,700,000

C: £37,000,000

D: £16,137,000

#### Written Solutions

This is a similar question to question 2.

If we know that $27\%$ represents $\pounds0.999$ million, the easiest way to calculate the total amount ($100\%$) is to work out $1\%$ first.

If $27\% = \pounds0.999$ million,

then

$1\% = \pounds0.999 \div 27 = \pounds0.037$ million.

If $1\%$ = $\pounds0.037$ million,

then

$100\%$ = $\pounds0.037 \times 100 = \pounds3.7$ million or $\pounds3,700,000.$

#### Question 4 In 2019, Mobile Warehouse sold products for HuaTec and Sumsang in the ratio of 3 : 2.  If sales of HuaTec and Sumsang accounted for 30% of Mobile Warehouse’s market share,  what was the value of the Mobile Warehouse’s HuaTec sales, if the combined market share for all 3 companies was £2.85 million?

A: £230,850

B: £598,500

C: £823,750

D: £955,000

#### Written Solutions

In 2019, we have been told that the total market share is worth $\pounds2.85$ million. The value of Mobile Warehouse’s market share was $45\%$, so the value of their share was:

$\pounds2.85 \times 0.45 = \pounds1.2825$ million.

Sales of Huatec and Sumsang accounted for $30\%$ of Mobile Warehouse’s sales, so the value of Huatec and Sumsang combined is:

$\pounds1.2825$ million $\times 0.3 = \pounds0.38475$ million.

If the sales of Huatec and Sumsang were in the ratio of $3 : 2$, this means that Huatec accounted for $\frac{3}{5}$ of the sales (we are dealing with fifths because the sum of the ratio is 5) , so the value of Huatec sales was:

$\pounds0.38474 \times \frac{3}{5} = \pounds0.230844$ or $\pounds230,850$

#### Question 5 What fraction of the annual red wine sales were generated in the 4th quarter?

A: 1/5

B: 1/4

C: 1/3

D: 2/3

#### Written Solutions

In quarter 1, there were 1600 bottles of red wine sold.

In quarter 2, there were 1200 bottles of red wine sold.

In quarter 3, there were 1000 bottles of red wine sold.

In quarter 4, there were 1900 bottles of red wine sold.

In total there were $1600 + 1200 + 1000 + 1900 = 5700$ bottles of red wine sold.

1900 out of the total of 5700 bottles sold were sold in quarter 4.

$\dfrac{1900}{5700}$ as a fraction can be simplified to $\dfrac{1}{3}$

Alternatively, you can type $1900 \div 5700$ into your calculator and you will get the answer $\frac{1}{3}$ or $0.\dot{3}$ (which hopefully you recognise as $\frac{1}{3}$)

This question can be simplified by ignoring the fact that the sales are in hundreds of bottles. By simply ignoring all the 00s, you will still arrive at the same answer:

$16 + 12 + 10 + 19 = 57$ $\dfrac{19}{57} = \dfrac{1}{3}$

#### Question 6 A bottle of red wine requires 24% more grapes than a bottle of white wine.  Given that the total number of grapes required to make white wine in the first and second quarters combined was 3,440,000, how many grapes were needed to produce all the red wine in quarter 4?

A: 950,000

B: 1,325,000

C: 1,884,800

D: 2,652,000

#### Written Solutions

In the first quarter, there were 2100 bottles of white wine sold.

In the second quarter, there were 2200 bottles of white wine sold.

In total there were $2100 + 2200 = 4300$ bottles of wine sold in quarters 1 and 2 combined.

If 3,440,000 grapes were used to produce 4300 bottle of wine, we can calculate the number of grapes required to produce one bottle of wine:}

$3,440,000 \div 4300 = 800$ grapes per bottle.

If red wine requires $24\%$ more grapes per bottle than white wine, then the number of grapes required to produce a bottle of red wine is:

$800 \times 1.24 = 992$ grapes

In quarter 4, 1900 bottles of red wine were produced, so the total number of grapes needed for the production of 1900 bottles is:

$1900 \times 992 = 1,884,800$

#### Question 7 A restaurant owner buys white and rosé wines from the Kookaburra vineyard in the ratio of 7: 2.  If the restaurant owner buys 360 bottles of rosé at a cost of A$9.95, what is the cost of a bottle of white wine if he spends A$17,253 in total on wine?

A: A$8.95 B: A$9.65

C: A$10.85 D: A$11.25

#### Written Solutions

The total expenditure on rosé wine if he buys 360 bottles is $360 \times \text{ A}\9.95 = \text{ A}\3582$

This means we can calculate the total expenditure on white wine:

$\text{ A}\17,253 - \text{ A}\3582 = \text{ A}\13,671$

Now we need to work out the number of bottles of white wine that he buys.

If the restaurant owner is buying white and rosé in the ratio of $7 : 2$, that means that $\frac{7}{9}$ of the wine he buys is white and $\frac{2}{9}$ is rosé (we are dealing in ninths because the sum of the ratio is 9).

We know that he has bought 360 bottles of rosé, so if this represents $\frac{2}{9}$ of the total, then we can work out that $\frac{1}{9}$ will be half this amount, so $\frac{1}{9}$ = 180 bottles.

If the sale of white wine and $\frac{7}{9}$ of the total and $\frac{1}{9}$ represents 180 bottles, then he has bought 1260 bottles.

A: £935

B: £1011

C: £1860

D: £2097

#### Written Solutions

In quarter 1, 1600 bottles of red wine are produced and are sold for A$9.65 per bottle, so the total vale of wine sold is: $1600 \times \text{ A}\9.65 = \text{ A}\15,440$ The value in pounds is: $\text{ A}\15,440 \div \text{ A}\1.67 = \pounds9245.51$ In quarter 2, 1200 bottles of red wine are produced and are sold for A$9.65 per bottle, so the total value of wine sold is:

$1200 \times \text{ A}\9.65 = \text{ A}\11,580$

The value in pounds is:

$\text{ A}\11,580 \div \text{ A}\1.62 = \pounds7148.15$

The difference between the value of red wine produced in quarter 1 and quarter 2 is:

$\pounds9245.51 - \pounds7148.15 = \pounds2097$ to the nearest pound.

#### Question 9 Which shares have had the biggest percentage increase between the average share price from 2018 to 2019?

A: BAE

B: BHP

C: GSK

D: HSBC

#### Written Solutions

First of all, it is worth checking that none of the share prices go down.

Secondly, M and S does not feature as an answer, so we don’t need to calculate this percentage increase.

BAE shares have increased from $\pounds468.20$ to $\pounds561.84$.

As a percentage increase, this is:

$\dfrac{\pounds561.84 - \pounds468.20}{\pounds468.20} \times 100 = 20\%$ increase.

BHP shares have increased from $\pounds1751.60$ to $\pounds2119.44$.

As a percentage increase, this is:

$\dfrac{\pounds2119.44 - \pounds1751.60}{\pounds1751.60} \times 100 = 21\%$ increase.

GSK shares have increased from $\pounds1523$ to $\pounds1858.06$.

As a percentage increase, this is:

$\dfrac{\pounds1858.06 - \pounds1523}{\pounds1523} \times 100 = 22\%$ increase.

HSBC shares have increased from $\pounds658.40$ to $\pounds776.91$.

As a percentage increase, this is:

$\dfrac{\pounds776.91- \pounds658.40}{\pounds658.40} \times 100 = 18\%$ increase.

Therefore GSK shares have increased the most.

#### Question 10 Bob has 320 shares invested in BAE, BHP and GSK in the ratio of 5 : 3 : 2.  What is the value of his share portfolio in 2019?  Give your answer to the nearest pound

A: £386,789

B: £396,880

C: £412,276

D: £568,234

#### Written Solutions

If Bob has shares with BAE, BHP and GSK in the ratio of $5 : 3 : 2$, this means that Bob has $\frac{5}{10}$ of his shares with BAE, $\frac {3}{10}$ with BHP and $\frac{2}{10}$ with GSK. (We are dealing in tenths because the sum of the ratio is 10). Of course, $\frac{5}{10}$ can be simplified to $\frac {1}{2}$, and $\frac{2}{10}$ can be simplified to $\frac{1}{5}$.

If Bob has a total of 320 shares, then we can calculate exactly how many he shares he has with each company.

Bob has $320 \times \frac{1}{2}$ shares with BAE $= 160$ shares. These shares have a value of $\pounds561.84$ each, so the total value of the BAE shares would be $\pounds561.84 \times 160 = \pounds89,894.40$

Bob has $320 \times \frac {3}{10}$ shares with BHP$= 96$ shares. These shares have a value of $\pounds2119.44$ each, so the total value of the BAE shares would be $\pounds2119.44 \times 96 = \pounds203,466.24$

Bob has $320 \times \frac {1}{5}$ shares with GSK $= 64$ shares. These shares have a value of $\pounds1858.06$ each, so the total value of the BAE shares would be $\pounds1858.06 \times 64 = \pounds118,915.84$

Therefore, the total value of Bob’s shares is:

$\pounds89,894.40 + \pounds203,466.24 + \pounds118,915.84 = \pounds412,276$ to the nearest pound.

#### Question 11 If M and S shares drop in value by 14% in 2020 and HSBC shares drop by 18% from 2019 values, what is the combined value of 85 shares of each?

A: £38,420

B: £41,273

C: £77,570

D: £82,675

#### Written Solutions

If M and S shares drop by 14% from $\pounds320.37$, then their new value will be:

$\pounds320.87 \times 0.86 = \pounds275.52$

85 M and S shares will therefore cost $\pounds275.52 \times 85 = \pounds23,419.08$

If HSBC shares drop by 18% from $\pounds776.91$, then their new value will be:

$\pounds776.91 \times 0.82 = \pounds637.07$

85 HSBC shares will therefore cost $\pounds637.07 \times 85 = \pounds54,150.63$

Therefore the combined costs of 85 shares of each in 2020 will be:

$\pounds23,419.08 + \pounds54,150.63 = \pounds77,570$

#### Question 12 Steve buys €138,410.24 of GSK shares in 2018.  What are they worth in pounds in 2019?

A: £106,003.98

B: £118,915.84

C: £122,687.26

D: £132,102.09

#### Written Solutions

If Steve buys €138,410.24 of shares in 2018, we can calculate what they are worth in pounds.

$€138,410.24 \div €1.42 = \pounds97,472$

If GSK shares are $\pounds1523$ each in 2018, then we can calculate how many shares Steve has bought:

$\pounds97,472 \div \pounds1523 = 64$ shares

In 2019, 64 shares in GSK are worth $64 \times \pounds1858.06 = \pounds118,915.84$

#### Question 13 How many mattresses are sold by all three salesmen combined in the months of February and March?

A: 52

B: 57

C: 66

D: 68

#### Written Solutions

To calculate the number of mattresses sold in February and March combined, we simply need to deduct the total number of mattresses sold up to the end of January from the total number of mattresses sold up to the end of March.

By the end of January, the 3 salesmen sold $6 + 8 + 9 = 23$ mattresses.

By the end of March, the 3 salesmen sold $30 + 26 + 24 = 80$ mattresses.

Therefore, in February and March, the 3 salesmen sold $80 - 23 = 57$ mattresses.

#### Question 14 What was the percentage increase in sales for salesman A from January to February?

A: 12.5%

B: 17%

C: 52.9%

D: 112.5%

#### Written Solutions

In January, salesman A sold 8 mattresses. In February, he sold $17 - 8 = 9$ mattresses.

As a percentage increase this is:

$\dfrac{9 – 8}{8} \times 100 = 12.5\%$

#### Question 15 On average, king-size mattresses account for 40% of sales, but these three salesmen manage to sell king-size mattresses 70% of the time.  How much additional revenue did they generate between January and March by ensuring that they sold king size mattresses 70% of the time and not 40% of the time?

A: £2,200

B: £2,800

C: £3,600

D: £4,800

#### Written Solutions

By the end of March, the 3 salesmen sold a total $30 + 26 + 24 = 80$ mattresses.

If 40% of the mattresses were king-size, then we can calculate the number of double and king-size mattresses they should have sold:

King-size = $80 \times 0.4 = 32$ (therefore $80 - 32 = 48$ doubles)

Therefore if they were selling at the average rate, they would have generated the following sales:

$(32 \times \pounds499) + (48 \times \pounds349) = \pounds32,720$

However, these salesman sold king-size mattresses 70% of the time, so we can calculate the number of double and king-size mattresses they did sell:

King-size = $80 \times 0.7 = 56$ (therefore$80 - 56 = 24$ doubles)

These salesman generated the following sales:

$(56 \times \pounds499) + (24 \times \pounds349) = \pounds36,320$

Therefore the additional revenue they generated as a result of upselling king-size mattresses was:

$\pounds36,320 - \pounds32,720 = \pounds3,600$

#### Question 16 Bonuses are paid at 15% of sales above £2500.  What was the bonus of salesman B in February if one third of his sales were double mattresses?

A: £185.08

B: £231.15

C: £362.75

D: £465.98

#### Written Solutions

We can work out that salesman B sold $18 - 9 = 9$ mattresses in February. If $\frac{1}{3}$ were double mattresses, then he sold 3 double mattresses and 6 king-size mattresses.

The cost of 3 doubles and 6 king-size is:

$(3 \times \pounds349) + (6 \times \pounds499) = \pounds4041$

Bonuses are paid at 15% above $\pounds2500$, so a 15% bonus is payable on $\pounds4041 - \pounds2500 = \pounds1541$ sales.

Therefore the bonus due is:

$\pounds1541 \times 0.15 = \pounds231.15$

#### Question 17 Due to the delicate ecosystem on Skomer Island, only 250 tourists are allowed to visit the island per day.  In April 2018, the full daily allocation of tourists landed on Skomer on 5/6 of the total number of days.  What was the mean amount of tourists that arrived on the remaining days?

A: 86

B: 115

C: 142

D: 212

#### Written Solutions

If the full allocation of tourists landed on Skomer Island on $\frac {5}{6}$ of the total number of days in April, then we can work out how many days in April the full allocation of 250 tourists landed:

$30 \text{ days} \times \frac{5}{6} = 25 \text{ days}$

In 25 days a total of $250 \times 25$ tourists arrived $= 6,200$ tourists.

If a total of 6,825 tourists arrived in total, then this means that $6,825 - 6,250 = 575$ tourists arrived on the remaining days.

There were $30 - 25 = 5$ remaining days in April, and 575 tourists arrived on these days, so now we can calculate the mean number of tourists per day:

$575 \div 5 = 115$ tourists

#### Question 18 The boat, the Dale Princess, transports tourists to Skomer Island and charges £12 per adult and £7 per child.  How much revenue did the Dale Princess make in June 2019 if 4/5 of the passengers were adults?

A: £62,735

B: £73,425

C: £79,865

D: £85,985

#### Written Solutions

In June 2019, there was a total of 6675 passengers. What we need to do is work out how many were adults and how many were children.

If $frac{4}{5}$ were adults, then the total number of adults was:

$6675 \times \frac{4}{5} = 5340$ adults

The remainder were therefore children, so there were $6675 - 5340 = 1335$ children.

If adults were charged $\pounds 12$ per ticket, then a total of $\pounds 12 \times 5340 = \pounds 64,080$ was generated.

If children were charged $\pounds 7$ per ticket, then a total of $\pounds 7 \times 1335 = \pounds 9,345$ was generated.

Therefore, the total revenue was $\pounds 9,345 + \pounds 64,080 = \pounds 73,425$

#### Question 19 The percentage increase in the number of tourists from 2017 – 2019 is the same as the percentage decrease of puffins nesting on the island in the same period.  If there were 31,560 puffins in 2017, how many were there in 2019?

A: 20,514

B: 26,786

C: 27,892

D: 29,564

#### Written Solutions

First of all, we need to work out what the percentage increase in the number of tourists was from 2017 – 2019.

In 2017, there were $4874 + 5318 + 5806 + 4102 = 20,100$ tourists.

In 2019, there were$6501 + 6922 + 6675 + 7037 = 27,135$ tourists.

As a percentage increase, this is:

$\dfrac{27,135 - 20,100}{20,100} \times 100 = 35\%$

This figure is the same figure for the percentage decrease in the number of puffins, so the population of puffins decreased by 35%. If there were 31,560 puffins in 2017, then we can calculate how many there were in 2019:

$31,560 \times 0.65 = 20,514$

#### Question 20 In June 2018, the boat only ran on 70% of the available days due to unfavourable weather.  If the boat is only allowed to deliver 250 passengers to the island on any day, and is fined £75 for each person over this limit, how much would the boat company incur in fines (assuming that on the days it did sail, it did not ever take fewer than 250 passengers)?

A: £32,675

B: £63,400

C: £75,900

D: £81,900

#### Written Solutions

In 2018, the price of oil was $80 and fell to$60 in 2019. As a percentage decrease, this is:

$\dfrac{(\80 - \60)}{\80}\times 100 = 25\%$ decrease

If the value of oil drops again by this percentage, then the value of a barrel of oil in 2020 will be:

$\60 \times 0.75 = \45$

Russia produced 11,200 hundreds of barrels in 2019, so if it increases its production by 10% in 2020, then Russia will produce:

$11,200 \times 1.1 = 12,230$ hundreds of barrels of oil $= 1,232,000$ barrels of oil.

The total value of the oil produced will therefore be:

$1,232,000 \times \45 = \55,440,000$