## 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

**Video Solutions**

**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.

**Video Solutions**

**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.

**Video Solutions**

**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

**Video Solutions**

**Question 5**

What fraction of the annual red wine sales were generated in the 4^{th} 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}

**Video Solutions**

**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**Video Solutions**

**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}\$13,671Now 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.

The restaurant owner has spent A$13,671 on white wine and has bought 1260 bottles, so the cost per bottle is:

\text{ A}\$13,671 \div 1260 = \text{ A}\$10.85**Video Solutions**

**Question 8**

What is the difference between the value of red wine produced in Q1 and Q2 in pounds if a bottle of red wine sells for A$9.65? Give your answer to the nearest pound.

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}\$15,440The value in pounds is:

\text{ A}\$15,440 \div \text{ A}\$1.67 = \pounds9245.51In 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}\$11,580The value in pounds is:

\text{ A}\$11,580 \div \text{ A}\$1.62 = \pounds7148.15The difference between the value of red wine produced in quarter 1 and quarter 2 is:

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

**Video Solutions**

**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.

**Video Solutions**

**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.

**Video Solutions**

**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 = \pounds275.5285 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 = \pounds637.0785 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**Video Solutions**

**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 = \pounds97,472If 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

**Video Solutions**

**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.

**Video Solutions**

**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\%**Video Solutions**

**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) = \pounds32,720However, 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) = \pounds36,320Therefore the additional revenue they generated as a result of upselling king-size mattresses was:

\pounds36,320 - \pounds32,720 = \pounds3,600**Video Solutions**

**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) = \pounds4041Bonuses 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**Video Solutions**

**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

**Video Solutions**

**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

**Video Solutions**

**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**Video Solutions**

**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 = \$45Russia 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