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Worked Solutions – Test 8 2021-02-05T14:15:51+00:00

## Worked Solutions – Test 8

#### Question 1

What was the mean number of sales made by Salesman A between January and May?

A: 18

B: 20

C: 23

D: 25

#### Written Solutions

Between January and May, Salesman A sold $20 + 23 + 26 + 22 + 25 = 116 \text{ sales}$

If this was the number of sales over a 5 month period, then the mean per month would be$116 \div 5 = 23.3$ or $23$ sales to the nearest whole number.

#### Question 2

To the nearest percentage, what was the mean percentage increase in sales from January – February for the three salesmen?

A: 21%

B: 25%

C: 26%

D: 32%

#### Written Solutions

Salesman A made 20 sales in January and 23 in February. As a percentage increase, this can be calculated as follows:

$\dfrac{23-20}{20} \times 100 = 15\%$

Salesman B made 16 sales in January and 18 in February. As a percentage increase, this can be calculated as follows:

$\dfrac{18-16}{16} \times 100 = \%12.5$

Salesman C made 14 sales in January and 21 in February. As a percentage increase, this can be calculated as follows:

$\dfrac{21-14}{14} \times 100 = \%50$

Therefore the mean percentage increase of the three salesman was $\dfrac{50 + 12.5 + 15}{3} = 25.83\%$ or $26\%$ to the nearest percentage.

#### Question 3

All 3 salesman increase their sales from May to June.  Salesman A’s sales increase by 20%, Salesman B’s by 50% and Salesman C’s by 25%?  If every sale generates a mean profit of £1,125, how much profit do the 3 salesman make in June?

A: £72,840

B: £86,625

C: £86,450

D: £86,782

#### Written Solutions

In May, Salesman A made 25 sales. If this increases by 20% in June, then the number of sales for June can be calculated as follows:

$25 \times 1.2 = 30 \text{ sales}$

In May, Salesman B made 18 sales. If this increases by 50% in June, then the number of sales for June can be calculated as follows:

$18 \times 1.5 = 27 \text{ sales}$

In May, Salesman A made 16 sales. If this increases by 25% in June, then the number of sales for June can be calculated as follows:

$16 \times 1.25 = 20 \text{ sales}$

Therefore in June there were a total of $30 + 27 + 20 = 77 \text{ sales}$

If each sale generated a profit of £1,125, then 77 sales would have generated 77 \times £1,125 = £86,625

#### Question 4

As a percentage of the total number of months, what proportion of Salesman C’s monthly sales exceeded the mean number of all three salesman’s sales per month?

A: 20%

B: 40%

C: 60%

D: 80%

#### Written Solutions

In January, there was a total of $20 + 16 + 14 = 50$ sales. The mean number of sales per salesman is $50 \div 3 = 16.7$. In January, Salesman C made 14 sales, so in January he sold less than the average salesman.

In February, there was a total of $23 + 21 +18 = 62$ sales. The mean number of sales per salesman is $62 \div 3 = 20.7$. In February, Salesman C made 21 sales, so in February he sold more than the average salesman.

In March, there was a total of $26 + 20 + 19 = 65$ sales. The mean number of sales per salesman is $65 \div 3 = 21.7$. In March, Salesman C made 19 sales, so in March he sold less than the average salesman.

In April, there was a total of $22 + 22 + 20 = 64$ sales. The mean number of sales per salesman is $64 \div 3 = 21.3$. In April, Salesman C made 22 sales, so in April he sold more than the average salesman.

In May, there was a total of $25 + 18 + 16 = 59$sales. The mean number of sales per salesman is $59 \div 3 = 19.7$. In May, Salesman C made 16 sales, so in May he sold less than the average salesman.

Salesman sold more than the average salesman in two of the five months. You many know that $\dfrac{2}{5} = 40\%$ but if not, you can simply calculate $2 \div 5 \times 100 = 40\%$

#### Question 5

In which fast-food establishment is the average spend per customer the highest?

A: Chicken Hut

B: Pizza Cottage

C: MacBurger

D: Phil’s Kebabs

#### Written Solutions

At Chicken Hut, £474,500 of revenue is generated by 73,000 customers. Therefore the average customer spend is $£474,500 \div 73,000 = £6.50$

At Pizza Cottage, £196,200 of revenue is generated by 36,000 customers. Therefore the average customer spend is $£196,200 \div 36,000 = £5.45$

At Mac Burger, £279,000 of revenue is generated by 45,000 customers. Therefore the average customer spend is $£279,000 \div 45,000 = £6.20$

At Phil’s Kebabs, £397,900 of revenue is generated by 46,000 customers. Therefore the average customer spend is $£397,900 \div 46,000 = £8.65$

Therefore Phil’s Kebab’s had the biggest average spend.

#### Question 6

What is the percentage value of the company with the highest outgoings as a percentage of total revenue?

A: 41%

B: 44%

C: 45.3%

D: 46%

#### Written Solutions

Chicken Hut’s outgoings are £215,000 and their revenue is £474,500. Their outgoings as a percentage of revenue is therefore $£215,000 \div £474,500 \times 100 = 45.41\%$

Pizza Cottage outgoings are £86,238 and their revenue is £196,200. Their outgoings as a percentage of revenue is therefore $£86.238 \div £196,200\times 100 = 43.95\%$

MacBurger outgoings are £114.390 and their revenue is £279,000. Their outgoings as a percentage of revenue is therefore $£ 114.390 \div £279,000\times 100 = 41\%$

Phil’s Kebabs outgoings are £183,034 and their revenue is £397,900. Their outgoings as a percentage of revenue is therefore $£183,034 \div £397,900 \times 100 = 46\%$

46% is therefore the percentage value of the highest percentage of outgoings.

#### Question 7

If, the following year, each fast-food retailer’s profit increases by 20%, how much profit is made by the 4 companies combined?

A: £756,936.45

B: £825,428.34

C: £898,725.60

D: £982,745.95

#### Written Solutions

Chicken Hut’s profit was $£474,500 - £215,000 = £259,500$. If the profit increases by 20%, then the profit for the following year will be $£259,500 \times 1.2 = £311,400$

Pizza Cottage’s profit was$£196,200 - £86,238 = £109,962$. If the profit increases by 20%, then the profit for the following year will be $£109,962 \times 1.2 = £131,954.40$

MacBurger’s profit was $£279,000 - £114,390 = £164,610$. If the profit increases by 20%, then the profit for the following year will be $£164,610 \times 1.2 = £197,532$

Phil’s Kebabs’ profit was $£397,900 - £183,034 = £214,866$. If the profit increases by 20%, then the profit for the following year will be $£214,866 \times 1.2 = £257,839.20$

The total profit combined of the 4 companies the following year will therefore be $£311,400 + £131,954.40 + £197,532 + £257,839.20 = £898,725.60$

#### Question 8

When a customer upgrades to a meal deal, this generates on average an additional £2.65 per customer.  By what percentage would the total revenue of the four companies combined have decreased by had there been no upgrades to meal deals?

A: 1.23%

B: 3.64%

C: 6.5%

D: 11.2%

#### Written Solutions

Chicken Hut had 2645 customers upgrading to the meal deal. If this generates £2.65 per customer, then they have generated $£2.65 \times 2645 = £7009.25$ additional revenue from meal upgrades.

Pizza Cottage had 956 customers upgrading to the meal deal. If this generates £2.65 per customer, then they have generated $£2.65 \times 956 = £2533.40$ additional revenue from meal upgrades.

MacBurger had 1264 customers upgrading to the meal deal. If this generates £2.65 per customer, then they have generated $£2.65 \times 1264 = £3349.60$ additional revenue from meal upgrades.

Phil’s Kebabs had 1398 customers upgrading to the meal deal. If this generates £2.65 per customer, then they have generated $£2.65 \times 1398 = £3704.70$ additional revenue from meal upgrades.

The total additional revenue generated by the 4 companies combined for meal upgrades was $£7009.25 + £2533.40 + £3349.60 + £3704.70 = £16,596.95$

The total revenue of the 4 companies combined was $£474,500 + £196,200 + £279,000 + £397,900 = £1,347,600$

Without the upgrades to meal deals, the companies would have lost out on £16,596.95. As a percentage of their total revenue, this would be $\dfrac{16,596.95}{1,347,600} \times 100 = 1.23\%$ to 2 decimal places.

#### Question 9

What was the difference between the total value of coins produced in 2016 and the total value of coins produced in 2017?

A: £1.2 million

B: £1.7 million

C: £1.8 million

D: £1.9 million

#### Written Solutions

In 2016, the value of the coins produced was:

$£2 \times 26 \text{ million} = £52 \text{ million}$ $£1 \times 649 \text{ million} = £649 \text{ million}$ $50\text{p} \times 46 \text{ million} = £23 \text{ million}$ $20\text{p} \times 213 \text{ million} = £42.60 \text{ million}$ $10\text{p} \times 135 \text{ million} = £13.50 \text{ million}$ $5\text{p} \times 306 \text{ million} = £15.30 \text{ million}$ $2\text{p} \times 186 \text{ million} = £3.72 \text{ million}$ $1\text{p} \times 368 \text{ million} = £3.68 \text{ million}$

Therefore, the total value of coins produced in 2016 was $£52 + £649 + £23 + £42.60 + £13.50 + £15.30 + £3.72 + £3.68 = £802.8 \text{ million}$

In 2017, the value of the coins produced was:

$£1 \times 750 \text{ million} = £750 \text{ million}$ $50\text{p} \times 68 \text{ million} = £34 \text{ million}$ $10\text{p} \times 33 \text{ million} = £3.3 \text{ million}$ $5\text{p} \times 221 \text{ million} = £11.05 \text{ million}$ $2\text{p} \times 17 \text{ million} = £0.34 \text{ million}$ $1\text{p} \times 241 \text{ million} = £2.41 \text{ million}$

Therefore, the total value of coins produced in 2017 was $£750 + £34 + £3.3 + £11.05 + £0.34 + £2.41 = £801.1$ million
Therefore the difference between the value of coins produced in 2016 and 2017 is $£802.8 - £801.1 = £1.7$ million

#### Question 10

To the nearest whole number, what was the percentage decrease in the value of 2p coins produced from 2016 to 2017?

A: 19%

B: 73%

C: 85%

D: 91%

#### Written Solutions

The fact that the question is asking for a percentage decrease in the value of the number of 2p coins produced makes no difference. We can simply work out the percentage decrease in the number of coins produced since the value of the coin is constant.

There were 186 million 2p coins produced in 2016 and 17 million in 2017. As a percentage decrease, this can be calculated as follows:

$\dfrac{186-17}{186} \times 100 = 90.86%$ or $91\%$ to the nearest whole number.

#### Question 11

The production of 10p and 5p coins between 2017 and 2018 further decreased by the same percentage as between 2016 and 2017.  What is the approximate combined value of the 10p and 5p coins produced in 2018?

A: £4.7 million

B: £6.2 million

C: £8.8 million

D: £9.2 million

#### Written Solutions

The production of 10p coins went from 135 million in 2016 to 33 million in 2017. As a percentage decrease this is:

$\dfrac{135-33}{135} \times 100 = 75.\dot{5}% \text{ decrease}$

Therefore if it continued to fall by the same rate in 2018, we can work out the number of 10p coins produced in 2018:

$33 \times 0.2\dot{4} = 8.0\dot{6} \text{ million}$$8.0\dot{6} \text{ million} \times 10p = £0.80\dot{6} \text{ million}$

The production of 5p coins went from 306 million in 2016 to 221 million in 2017. As a percentage decrease this is:

$\dfrac{306-221}{306} \times 100 = 27.\dot{7}% \text{ decrease}$

Therefore if it continued to fall by the same rate in 2018, we can work out the number of 5p coins produced in 2018:

$221 \times 0.7\dot{2} = 159.6\dot{1} \text{ million}$$159.6\dot{1} \text{ million} \times 5p = £7.980\dot{5} \text{ million}$$£7.980\dot{5} \text{ million} + £0.80\dot{6} \text{ million} = £8.8 \text{ million}$to the nearest given approximation (we don’t need to be massively accurate during the preceding calculations to arrive at this answer, so we can round previous answers and ignore the recurring digit).

#### Question 12

The mintage figures showed that there were 6,400,000 2016 Team GB 50p coins produced and 88,000,000 2001 Britannia 50p coins produced.  What was the ratio of the production of Team GB 50p coins to 2001 Britannia 50p coins?

A: 1 : 8.75

B: 1 : 13.75

C: 1 : 14.2

D: 1 : 16.68

#### Written Solutions

The ratio of Team GB : Britannia can be expressed as $6,400,000 : 88,000,000$. We can simplify this to $64 : 880$

Since the answer options all have the figure 1 as the first ration share, we need to think how we reach 1 from 64. Fairly easy, you divide by 64. So if we divide the first ratio share by 64, then we have to divide the second ratio share by 64 as well in order to have an equivalent ratio:

$64 : 880$$= 64 \div 64: 880 \div 64$$= 1 : 13.75$

#### Question 13

The total budget for the Art Department was £6,500 in 2011 and increased by 5% by 2012.  In neither year did the Art Department spend its full budget.  What is the amount of money left unspent in this two-year period?

A: £2725

B: £2845

C: £3285

D: £3825

#### Written Solutions

In 2011, the budget was £6,500 and the Art Department spent $£2400 + 800 + 1200 + 1500 = £5900$

Therefore the amount unspent in 2011 was $£6500 - £5900 = £600$

If the total budget for the Art Department was £6,500 and increased by 5% for the following year, we can work out what the budget for 2012 increased to:

$£6,500 \times 1.05 = £6,825$

In 2012, the Art Department spent $£1800 + £900 + £800 + £1200 = £4700$

Therefore the amount unspent in 2012 was $£6825 - £4700 = £2125$

Therefore the amount unspent over the two-year period was $£2125 + £600 = £2725$

#### Question 14

From 2014 to 2015, the Art Department increased spending in supplies by 8% and model hire by 5%, and increased spending on room hire by £200.  The spending for socials remained the same.  What was the percentage increase in overall spending to one decimal place?

A: 6.3%

B: 7.4%

C: 10.7%

D: 12.9%

#### Written Solutions

In 2014, the Art Department spent £2000 on supplies. If this increased by 8% in 2015, then the new amount spent on supplied would be:

$£2000 \times 1.08 = £2160$

Model hire was £1100, so if this increased by 5%, then the new value would be:

$£1100 \times 1.05 = £1155$

If room hire increased by £200, then the new value would be $£600 + £200 = £800$

Socials remained the same at £1900

Therefore, the total spending for 2015 was $£2160 + £1155 + £800 + £1900 = £6015$

In 2014, the total spending was $£2000 + £600 + £1100 + £1900 = £5600$

Therefore spending increased from £5600 to £6015. As a percentage increase, this is:

$\dfrac{£6015-£5600}{£6015} \times100 = 7.4\%$

#### Question 15

In 2011, the Art Department had 25 members.  By 2014 the number of members increased by 20%.  What was the difference between the average spend per person on socials in 2011 and 2014 to the nearest pound?

A: £3

B: £5

C: £6

D: £8

#### Written Solutions

If the Art Department had 25 members in 2011 which I ncreased by 20%, then in 2014 there the new number of members can be calculated as follows:

$25 \times 1.2 = 30 \text{ members}$

In 2011, £1500 was spent on socials. If there were 25 members, then the average spend per person on socials was $£1500 \div 25 = £60$

In 2014, £1900 was spent on socials. If there were 30 memebrs, then the average spend per person on socials was $£1900 \div 30 = £63.33$

Therefore the difference between the two years was £3

#### Question 16

Money spent on supplies is split between paints, paper and canvasses in the ratio of 6 : 4 : 5.  What is the amount of money spent on paints in 2015 if the amount spent on supplies increases by 12% from 2014?

A: £685

B: £896

C: £912

D: £980

#### Written Solutions

If the money spent on supplies is split between paints, paper and canvasses in the ratio of 6 : 4 : 5, this means that $\dfrac{6}{15}$ of the money was spent on paints, $\dfrac{4}{15}$ on paper and $\dfrac{5}{15}$ on canvasses. (We are dealing in fifteenth because $6 + 4 + 5 = 15$.)

The amount spent on supplies in 2014 is £2000 and this figure increases by 12%, then the new amount will be:

$£2000 \times 1.12 = £2240$

If $\dfrac{6}{15}$ was spent on paints, then the amount spent on paints was:

$\dfrac{6}{15} \times £2240 = £896$

#### Question 17

What is the difference in the value of beef, if sold in dollars, from quarter 1 to quarter 4?

A: $12,460 B:$13,230

C: $18.995 D:$24,180

#### Written Solutions

In quarter 1, total sales were £525,000 and beef accounted for 27% of this. Therefore the value of beef was:

$£525,000 \times 0.27 = £141,750$

In dollars this would be:

$£141,750 \times \1.32 = \187,110$

In quarter 4, total sales were £675,000 and beef accounted for 23% of this. Therefore the value of beef was:

$£675,000 \times 0.23 = £155,250$

In dollars this would be:

$£155,250 \times \1.12 = \173,880$

Therefore the difference in the value of beef from quarter 1 to quarter 4 is:

$\187,110 - \173,880 = \13,230$

#### Question 18

If there had not been an outbreak of swine flu, the value of quarter 4 pork sales would have been 35% greater than value reported.  How much, in dollars, was the cost of the swine flu outbreak?

A: $13,475 B:$18,646

C: $20,879 D:$21,168

#### Written Solutions

In quarter 4, total sales were £675,000 and pork accounted for 8% of this. Therefore the value of pork was:

$£675,000 \times 0.08 = £54,000$

If the figure should have been 35% more than this, then the value of missed pork sales was:

$£54,000 \times 0.35 = £18,900$

In dollars this would be:

$£18,900 \times \1.12 = \21,168$

#### Question 19

To the nearest whole number, what was the percentage increase in the value of chicken and eggs combined from quarter 1 to quarter 4?

A: 29%

B: 37%

C: 46%

D: 52%

#### Written Solutions

In quarter 1, total sales were £525,000 and chicken and eggs accounted for 50% of this. Therefore the value of chicken and eggs was:

$£525,000 \times 0.5 = £262,500$

In quarter 4, total sales were £675,000 and chicken and eggs accounted for 59% of this. Therefore the value of chicken and eggs was:

$£675,000 \times 0.59 = £398,250$

So the combined value of chicken and eggs increased from £262,500 to £398,250.

As a percentage increase this can be calculated as follows:

$\dfrac{£398,250-£262,500}{£262,500} \times 100 = 51.7%$ or $52\%$ to the nearest whole number.

#### Question 20

A supermarket chain buys 67,500 litres of milk from the supplier in quarter 4 which represents 30% of the total amount of milk produced.  How much does the supermarket pay for a litre of milk?

A: 45p

B: 52p

C: 60p

D: 64p

#### Written Solutions

If 67,500 litres represents 30% of the total milk produced, we need to work out how many litres of milk are produced in total.

If $67,500 = 30\%$

Then $67,500 \div 30 = 1\%$

So $100\% = 67,500 \div 30 \times 100 = 225,000 \text{ litres}$

In quarter 4, total sales were £675,000 and milk accounted for 20% of this. Therefore the value of milk was:

$£675,000 \times 0.2 = £135,000$

If 225,000 litres of milk cost £135,000, then one litre of milk would cost $£135,000 \div 225,000 = £0.6$ or $60\text{ p}$.