FreePhone: 020 3633 5134
Worked Solutions – Test 4 2021-02-05T14:13:55+00:00

## Worked Solutions – Test 4

#### Question 1

What was the percentage decrease (correct to 1 decimal place) in total salary for Simon and Peter combined from June to July?

A: 6.8%

B: 9.2%

C: 12.7%

D: 17.1%

#### Written Solutions

In June, Simon and Peter’s combined salary was $\pounds1400 + \pounds1560 = \pounds2960$.

In July, Simon and Peter’s combined salary was $\pounds1240 + \pounds1520 = \pounds2760$

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

$\dfrac{\pounds2960 - \pounds2760}{\pounds2960} \times100 = 6.8\%$ correct to one decimal place.

#### Question 2

What is Wendy’s take home pay in June if she is taxed at 20% on everything she earns above £950?

A: £1128

B: £1150

C: £1356

D: £1470

#### Written Solutions

Wendy’s salary in June is $\pounds1600$. If she is taxed at $20\%$ on her salary above $\pounds950$, then we need to work out her taxable income:

$\pounds1600 - \pounds950 = \pounds650$ taxable income.

If she is taxed at $20\%$ on this, then the amount she pays in tax can be calculated as follows:

$\pounds650 \times0.2 = \pounds130$.

Therefore if she pays $\pounds130$ tax from her $\pounds1600$ salary, then she is paid a total of $\pounds1600 - \pounds130 = \pounds1470$

#### Question 3

As a percentage to the nearest whole number, how much less was Dan paid between June and August than Peter?

A: 28%

B: 29%

C: 42%

D: 53%

#### Written Solutions

Between June and August, Dan is paid $€1125 + €1175 + €1150 = €3450$

In pounds, this can be calculated as follows:

$€3450 \div €1.25 = \pounds2760$

Between June and August, Peter is paid $\pounds1560 + \pounds1520 + \pounds1640 = \pounds4720$

If Dan is paid $\pounds2760$ and Peter is paid $\pounds4720$, this is a difference of $\pounds4720 - \pounds2760 = \pounds1960$.

$\pounds1960$ as a percentage of Peter’s pay of $\pounds4720$ is:

$\dfrac{\pounds1960}{\pounds4720} \times100 = 41.5\%$ or $42\%$ to the nearest whole number.

#### Question 4

Peter needs to repay £180 per month from his pre-tax salary for a bike and is then taxed at 20% on everything above £950 per month.  If he pays £400 per month for rent and bills, how much does he spend on food in this 3 month period if he spends 35% of his remaining salary on food?

A: £627.84

B: £680.45

C: £790.95

D: £949.90

#### Written Solutions

Peter’s salary for the period June – August is $\pounds1560 + \pounds1520 + \pounds1640 = \pounds4720$. Before he is taxed $\pounds180$ per month is deducted. Since this is a period of 3 months, we need to deduct $3\times\pounds180 = \pounds540$ from his pre-tax salary.

$\pounds4720 - \pounds540 = \pounds4180$

If Peter is taxed on everything above $\pounds950$ per month, then we can work out his taxable income by simply subtracting $\pounds950\times3 = \pounds2850$ from the $\pounds4180$:

$\pounds4180 - \pounds2850 = \pounds1330$

If he is taxed at $20\%$ on $\pounds1330$, then he will pay $0.2\times\pounds1330 = \pounds266$ in tax.
Therefore his pay for the three month period is:

$\pounds4180 - \pounds266 = \pounds3914$

We also need to deduct three month’s worth of rent and bills which is $3\times\pounds400 = \pounds1200$:

$\pounds3914 - \pounds1200 = \pounds2714$

If he spends $35\%$ of his salary on food, then we can calculate exactly how much he spends on food over the three month period:

$\pounds2714\times0.35 = \pounds949.90$

This is quite a long question but, by not deleting answers in your calculator, you will save time by not having to re-enter the starting number in every calculation.

#### Question 5

The stated price of a holiday to Cyprus increases by 27%.  What is the overall percentage increase of the holiday for a family of four, factoring in the costs of flights and food?

A: 16%

B: 19%

C: 23%

D: 27%

#### Written Solutions

The stated holiday price to Cyprus is $\pounds2640$. If this increases by $27\%$, then its new price will be:

$\pounds2650\times1.27 = \pounds3365.50$

If we add in the costs of flights and food on top of this increases price, we can determine how much the overall holiday costs.

$\pounds3365.50 + \pounds420 + (\pounds24\times7\times4) = \pounds4457.50$

The original holiday would have cost:

$\pounds2650 + \pounds420 + (\pounds24\times7\times4) = \pounds3742$

The percentage increase in the cost of the holiday can be calculated as follows:

$\dfrac {\pounds4457.50 - \pounds3742}{\pounds3742} \times100 = 19.12\%$ or $19\%$ to the nearest whole number.

#### Question 6

Two people split the holiday price of a holiday to Portugal in the ratio of 2 : 3.  All other costs are shared evenly.  What is the overall ratio of cost between the two people?

A: 3 : 7

B: 8 : 11

C: 77 : 59

D: 103 : 121

#### Written Solutions

The holiday price for a holiday for two people to Portugal is $€450\times2 = €900$.

If this is split in the ratio of 2 : 3, then that means that one person will pay $\frac{2}{5}$ of the amount and the other will pay $\frac{3}{5}$. (We are dealing with fifths because 2 + 3 = 5)

Therefore the person paying $\frac{2}{5}$ will pay:

$€900\times \frac{2}{5} = €360$

The other person will pay $€900 - €360 = €540$

Flights cost €250 for 2 people. If this cost is shared evenly, then each person will pay €125.

Meals are €15 per person per night, so for a week, food will cost $€15\times7 = €105$.

In total, one person will pay $€105 + €125 + €360 = €590$

The other person will pay $€105 + €125 + €540 = €770$

Therefore the ratio of what they pay is 770 : 590 which can easily be simplified to 77 : 59.

#### Question 7

The Portugal deal is amended at the last minute.  The holiday price is reduced by 15%, the flight cost remains the same and the food is included for free.  How much savings can be made to the nearest pound for a holiday for 4 people for 7 nights?

A: £490

B: £539

C: £690

D: £820

#### Written Solutions

If the Portugal price has been reduced by $15\%$, then the new holiday price can be calculated as follows:

$€450\times0.85 = €382.50$

This is a saving of $€450 - €382.50 = €67.50$ per person.

If there are four people going on holiday, then this is a saving of $€67.50\times4 = €270.$

If the food is free, then this is another saving:

$€15\times7\times4 = €420$

Therefore the total savings come to a total of $€420 + €270 = €690$

All we need to do now is to convert this to pounds:

$€690 \div €1.28 = \pounds539$ to the nearest pound.

#### Question 8

A couple book a holiday to Italy and share the overall cost.  How much does the holiday cost them each to the nearest pound?

A: £956

B: £1064

C: £1030

D: £1271

#### Written Solutions

The only thing which makes this question complicated is that the food is in euros.

The total cost of the food is $€22\times2\times21 = €924$

Now we need to convert the €924 into pounds:

$€924 \div €1.28 = \pounds721.88$

For 2 people, the holiday costs $\pounds1500 + \pounds320 + \pounds721.88 = \pounds2541.88$, so will therefore cost half this amount per person, so the final answer is $\pounds1271$ to the nearest pound.

#### Question 9

To the nearest pound, what is the difference between the annual wages of a VP in the two banks if there are 2500 VPs in Silverman Bank and 2038 in Credit French?

A: £16,786

B: £29,987

C: £143,784

D: £202,958

#### Written Solutions

At Silverman Bank, VPs comprise $16\%$ of the staff. If the total cost of Silverman’s staff is $\pounds8.4$ billion, then the amount assigned to VPs is:

$\pounds8.4$ billion$\times 0.16 = \pounds1.344$ billion

If there are 2500 VPs at Silverman’s bank, then we can calculate the wages of one VP as follows:

$\pounds1.344$ billion $\div 2500 = \pounds537,600$

At Credit French, VPs comprise $11\%$ of the staff. If the total cost of Silverman’s staff is $\pounds 6.2$ million, then the amount assigned to VPs is:

$\pounds6.2$ billion $\times0.11 = \pounds0.682$ billion

If there are 2038 VPs at Silverman’s bank, then we can calculate the wages of one VP as follows:

$\pounds0.682$ billion $\div 2038 = \pounds334,641.81$

The difference in pay between VPs at the two banks is $\pounds537,600 - \pounds334,641.81 = \pounds202,958$ to the nearest pound.

#### Question 10

What is the ratio of spending of wages on analysts for Silverman Bank and Credit French?

A: 3: 5

B: 6: 7

C: 28: 31

D: 43: 49

#### Written Solutions

Analysts comprised $8\%$ of Silverman. If the total cost of Silverman’s staff is $\pounds8.4$ billion, then the amount assigned to analysts is:

$\pounds8.4$ billion$\times 0.08 = \pounds0.672$ billion

Analysts comprised $12\%$ of Credit French. If the total cost of Credit French’s staff is $\pounds6.2$ billion, then the amount assigned to analysts is:

$\pounds6.2$ billion $\times 0.12 = \pounds0.744$ billion

The ratio of spending is $\pounds0.672$ billion $: \pounds0.744$ billion. We can simplify this ratio with minimal effort to $672 : 744$.

$\dfrac{672}{744} = \dfrac {28}{31}$

If you type $672 \div 744$ into your calculator, your calculator may even give you the answer of $\dfrac {28}{31}$, otherwise you will need to simplify the fraction $\dfrac{672}{744}$ until you eventually reach of $\dfrac {28}{31}$

#### Question 11

Silverman want to decrease spending on directors to 10% of overall wages.  Assuming that overall staffing costs will remain the same, how many directors do they need to make redundant if they are paid £1,425,000 each?

A: 85

B: 96

C: 102

D: 118

#### Written Solutions

Silverman’s spending on directors is currently $12\%$. $12\%$ of the total staffing costs of $\pounds8.4$ billion can be calculated as follows:

$0.12\times\pounds8.4$ billion = $\pounds1.008$ billion.

If Silverman want to reduce this figure to $10\%$ and keep overall staffing costs the same, then directors will cost a total of:

$0.1 \times \pounds8.4$ billion = $\pounds0.84$ billion

This means that they will have saved a total of $\pounds1.008$ billion $- \pounds0.84$ billion $= \pounds0.168$ billion. At this stage it might be worth converting $\pounds0.168$ billion to $\pounds168,000,000$

If each director costs the firm $\pounds1,425,000$ , we can calculate the number of directors they need to get rid of as follows:

$\pounds168,000,000 \div \pounds1,425,000 = 117.89$ directors.

Since it is not possible to make 117.89 directors redundant to meet this cost saving, they will need to make 118 redundant.

#### Question 12

If Credit French promote half of their analysts to associates, how much do associates earn if, following this promotion, there are now 34,720 associates?

A: £63,000

B: £75,000

C: £83,000

D: £102,000

#### Written Solutions

Analysts comprise $12\%$ of the work force at Credit French. If half of them are promoted to associates, then this means that $6\%$ of the overall workforce are promoted so the overall percentage of associates will move from $36\%$ to $42\%$.

If the staffing costs are $\pounds6.2$ billion and $42\%$ are associates, then this means that the overall cost of associates is:

$\pounds6.2$ billion$\times 0.42 = \pounds2.604$ billion

If this represents 34,720 associates, then we can now calculate how much one associate earns:

$\pounds2.604$ billion $\div 34,720 = \pounds75,000$

(This answer is probably easier to calculate if you convert $\pounds2.604$ billion to $\pounds2,604,000,000$ first or simply multiply your answer by a billion (1,000,000,000).)

#### Question 13

Over the 4 year period, sales of DVDs are split between kids DVDs and adult DVDs in the ratio of 1 : 3.  How many adult DVDs were sold in total?

A: 7790

B: 9320

C: 16,840

D: 23,370

#### Written Solutions

In 2016, DVDs comprised $22\%$ of overall sales. If there were 32,200 sales in total, then we can calculate the number of DVD sales as follows:

$32,200\times0.22 = 7084$

In 2017, DVDs comprised $28\%$ of overall sales. If there were 28,100 sales in total, then we can calculate the number of DVD sales as follows:

$28,100\times0.28 = 7868$

In 2018, DVDs comprised $32\%$of overall sales. If there were 31,300 sales in total, then we can calculate the number of DVD sales as follows:

$31,300\times0.32 = 10,016$

In 2019, DVDs comprised $18\%$ of overall sales. If there were 34,400 sales in total, then we can calculate the number of DVD sales as follows:

3$4,400\times0.18 = 6192$

Therefore in total there were $7084 + 7868 + 10,016 + 6192 = 31,160$ DVD sales.

If this was split in the ratio of $1 : 3$, then this means that adult DVDs accounted for $\frac{3}{4}$ of overall sales (we are dealing in quarters because $1 + 3 = 4$).

$31,160\times\frac{3}{4} = 23,370$

#### Question 14

CDs sold for an average of £6.92, £7.12 and £6.86 in 2017, 2018 and 2019 respectively.  How much profit was made on CD sales if the total cost of buying the CDs was £55,000?

A: £37,757.44

B: £53,485.44

C: £67,355.20

D: £122,355.20

#### Written Solutions

First of all, we need to work out how many CDs were sold in each year.

In 2017, CD sales were $16\%$ of overall sales, so the number of CD sales was $0.16\times 28,100 = 4496$. At an average selling price of $\pounds6.92$, the total of CD sales is:

$\pounds6.92\times4496 = \pounds31,112.32$

In 2018, CD sales were $24\%$ of overall sales, so the number of CD sales was $0.24\times31,300 = 7512$. At an average selling price of $\pounds7.12$, the total of CD sales is:

$\pounds7.12 \times 7512 = \pounds53,485.44$

In 2019, CD sales were $16\%$ of overall sales, so the number of CD sales was $0.16\times34,400 = 5504$. At an average selling price of$\pounds6.86$, the total of CD sales is:

$\pounds6.86\times5504 = \pounds37,757.44$

The total CD sales for this 3 year period came to:

$\pounds31,112.32 + \pounds53,485.44 + \pounds37,757.44 = \pounds122,355.20$. If you deduct the cost of buying the CDs, the overall profit was:

$\pounds122,355.20 - \pounds55,000 = \pounds67,355.20$

#### Question 15

In 2016, the average profit made on a game was £13.15.  56% of the overall profit in 2016 was from sales of games.  How much profit was made for CDs, DVDs and games combined in 2016?

A: £71,136.24

B: £135,879.86

C: £362,940

D: £687,995.72

#### Written Solutions

First of all, we can work out how many games were sold. Games were $48\%$ of the overall 32,200 units, so:

$0.48 \times 32,200 = 15,456$ games sold.

If the average profit was $\pounds13.15$ per game, then the total profit would be:

$\pounds13.15\times15,456 = \pounds203,246.40$

If $\pounds203,246.40$ represents $56\%$

then:

$1\% = \pounds203,246.40 \div 56 = \pounds3629.40$

so:

$100\% = \pounds3629.40\times100 = \pounds362,940$

#### Question 16

In 2020, Devil Music expect sales to increase by the same percentage as the percentage increase in sales (rounded to the nearest percentage point) from 2018 to 2019.  If sales of games increase from 66% to 75% of overall sales, and profit of £16.45 is made on each game sold, how much profit will Devil Music make on games in 2020?

A: £146,985

B: £285,936

C: £466,851

D: £563,962

#### Written Solutions

Sales increased from 31,300 to 34,400. As a percentage, this can be calculated as:

$\dfrac{34,400 - 31,300}{31,300} \times100 = 9.9\%$ (rounded to $10\%$)

Therefore sales have increased by $10\%$.

If sales again increase by $10\%$ from 2019 – 2020, then the number of units sold in 2020 is:

$34,400\times1.1 = 37,840$

If $75\%$ of sales is made from games, then we can calculate the number of games sold:

$37,840\times0.75 = 28,380$

If the company makes $\pounds16.45$ per game, then they will make $\pounds16.45\times28,380 = \pounds466,851$ profit in total.

#### Question 17

What is the value of 1 Australian dollar in euros in May?

A: €0.32

B: €0.45

C: €0.50

D: €0.57

#### Written Solutions

First of all, we can calculate what $1\text{A}\$ is worth in pounds:

$1\text{A}\ \div 1.97\text{A}\ = \pounds0.5076$

Now we can convert the pound value to euros:

$\pounds0.5076$ is worth $\pounds0.5076\times €1.12 = €0.57$

#### Question 18

A businessman buys £5,000 of euros in January which he then trades back to euros in February.  What profit has he made to the nearest pound?

A: £32

B: £43

C: £68

D: £124

#### Written Solutions

If the businessman exchanges $\pounds5,000$ into euros in January, we need to calculate how many euros he receives:

$\pounds5,000 \times €1.16 = €5,800$

If he trades these back into euros in February, he will receive:

$€5,800 \div €1.15 = \pounds5043$ (to the nearest pound).

Therefore, the businessman has made a profit of $\pounds43$.

#### Question 19

If the value of the Yen continues to fall at the same rate per month as the mean percentage per month between January and May (correct to 2 decimal places), what will the Yen be worth in June?  Give your answer to the nearest Yen.

A: 137 Yen

B: 138 Yen

C: 139 Yen

D: 140 Yen

#### Written Solutions

First of all, we need to work out the percentage decrease in the value of the Yen month by month.

From January to February, the percentage decrease was $\dfrac{156 – 152}{156} = 2.56\%$ decrease (correct to 2 decimal places)

From February to March, the percentage decrease was $\dfrac{152 – 148}{152} = 2.63\%$ decrease (correct to 2 decimal places)

From March to April, the percentage decrease was $\dfrac{148 – 145}{148} = 2.03\%$decrease (correct to 2 decimal places)

From April to May, the percentage decrease was $\dfrac{145 – 142}{145} = 2.07\%$ decrease (correct to 2 decimal places)

Therefore, the mean percentage decrease was $\dfrac{2.56 + 2.63 + 2.03 + 2.07}{4} = 2.32\%$

Therefore, if the Yen falls by $2.32\%$ from May to June, the Yen will be worth:

$142\times0.9768 = 138.7056$ Yen or $139$ to the nearest Yen

#### Question 20

A traveller converts £2,500 into Yen and £2,500 into Australian dollars in March before going on holiday.  If he spends 85% of the Yen and 78% of the Australian dollars, what is the difference (to the nearest pound) between the value of the remaining Yen and Australian dollars when he converts them back to pounds in May?

A: £86

B: £158

C: £170

D: £306

#### Written Solutions

First of all, we need to convert $\pounds2,500$ into Yen and $\pounds2,500$ into Australian dollars.

$\pounds2,500\times148$ Yen = $370,000$ Yen

$\pounds2,500\times \text{ A}\2.01 = \text{ A}\5,025$

If he spends $85\%$ of the Yen, then he has $15\%$ remaining.

$0.15\times370,000$ Yen = $55,500$ Yen remaining

55,500 Yen in pounds is:

$55,500$ Yen $\div 142$ Yen $= \pounds390.85$

If he spends $78\%$ of the Australian dollars, he has $22\%$ remaining.

$0.22 \times \text{ A}\5,025 = \text{ A}\1105.50$

A\$1105.50 in pounds is:

$\text{ A}\1105.50 \div \text{ A}\1.97 = \pounds561.16$

The difference between the values of the remaining currency is:

$\pounds561.16 - \pounds390.85 = \pounds170.31$ or $\pounds170$ to the nearest pound.