The South African taxi association, Transaction Capital, published its results for the current state of the South African minibus taxi industry for the year ended September 2019 - NSC Mathematical Literacy - Question 4 - 2021 - Paper 2
Question 4
The South African taxi association, Transaction Capital, published its results for the current state of the South African minibus taxi industry for the year ended Se... show full transcript
Worked Solution & Example Answer:The South African taxi association, Transaction Capital, published its results for the current state of the South African minibus taxi industry for the year ended September 2019 - NSC Mathematical Literacy - Question 4 - 2021 - Paper 2
Step 1
4.1.1 Determine, to the nearest thousand, the number of buses needed to replace the minibus taxis.
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Answer
To find the number of buses needed, use the formula:
extNumberofbuses=13.2Number of minibus taxis
Substituting the number of minibus taxis:
Number of buses=13.2250000≈18939.39
Rounding to the nearest thousand:
Number of buses≈19000
Step 2
4.1.2 (a) Calculate (in euros) the difference in net worth of the minibus taxi industry using exchange rates A and B.
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To calculate the difference in net worth between the two exchange rates, apply the formula:
Difference=Net worth at Rate A−Net worth at Rate B
First, convert R50 billion to euros using each exchange rate:
Using Exchange Rate A:
Net worth at A=15.89750000000000≈3141380861.76 euros
Using Exchange Rate B:
Net worth at B=15.96672850000000000≈3124976868.64 euros
4.1.2 (b) Justify which exchange rate (A or B) they should use when doing the presentation to their European clients.
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Transaction Capital should use Exchange Rate A during their presentation. This exchange rate results in a higher net worth when converted into euros, which is advantageous for illustrating the potential value to European businessmen. It reflects a more favorable financial position, making it more appealing in a business context.
Step 4
4.1.3 Calculate the number of commuters who do NOT use a minibus taxi.
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The ratio of daily commuter trips is given as:
Train : Bus : Minibus taxi=4:5:7
Let the total number of commuter trips be represented as:
Total trips=15extmilliontrips
Calculating the proportion for each category:
Train trips:
Train trips=164×15000000=3750000exttrips
Bus trips:
Bus trips=165×15000000=4687500exttrips
Minibus taxi trips:
Minibus taxi trips=167×15000000=6562500exttrips
The total using a minibus taxi is 6562500. Now, calculate the number of commuters who do NOT use a minibus taxi:
Total commuters NOT using minibus taxi=15000000−6562500=8437500
Step 5
4.1.4 Verify, showing ALL calculations, whether the statement is valid.
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Answer
To verify the distance traveled by minibus taxis in one year,
Calculate the annual distance:
Annual distance=19 billion km=19,000,000,000extkm
Next, calculate the distance to the moon and back:
Distance to the moon = 384,402 km
Total distance for 24,000 trips:
Total distance to Moon=24000×(2×384402)=24000×768804=18499296000extkm
Comparing the distances:
Since 18499296000 km > 19000000000 km, the statement is valid.
Step 6
4.2.1 Write down the total number of days covered by the period shown in ANNEXURE C.
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Answer
The total number of days between 9 January 2015 and 3 January 2020 can be calculated as:
From 9 January 2015 to 9 January 2020 is 5 years, which is 1826 days (including 1 leap year).
Subtracting the period from 9 January to 3 January is 6 days.
Therefore, total days = 1826 - 6 = 1820 days.
Step 7
4.2.2 Determine (in cents) the value of a share on 9 January 2015.
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Answer
Given that the value of a share on 3 January 2020 is known, calculate:
If shares on 3 January 2020 = R12,68
Value on 9 January 2015:
Value=12.68−R12.68=R0extcents
Step 8
4.2.3 Verify, showing calculations, whether the following statements are CORRECT:
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Answer
Calculate the percentage change in the share price:
If the price reduced by 3.51%, and starting from an earlier value, we find the total calculated amount to check if it results in the correct share price. Also cross-check the 80% statistics about share price increment at the year's commencement period. Analyze these data points to establish whether they hold true.
Step 9
4.2.4 Calculate (in rand) the profit a person will make if he/she bought 5 000 shares.
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First, find the lowest price in which shares are bought, then find the sell price and calculate profit as:
Profit=(Sell Price - Purchase Price)×Number of Shares
Express profit in rand once calculations are completed based on the mathematical representation of selling at a higher price.
