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SLIDE 1
A corridor is 2 metres wide and 9 metres long. The ratio of the width to the length is .
This is read “2 to 9”.
? What is the ratio of the width to the length of this rectangle?
? What is the ratio of the base to the height of this triangle?
SLIDE 2
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?
SLIDE 1B
A corridor is 2 yards wide and 9 yards long. The ratio of the width to the length is .
This is read “2 to 9”.
? What is the ratio of the width to the length of this rectangle?
? What is the ratio of the base to the height of this triangle?
SLIDE 2B
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?
SLIDE 3
Ratios are fractions and vice-versa.
To express a ratio in its simplest terms means to cancel it down.
Example
Express the ratio 5:25 in its simplest terms. Express it as a fraction.
Exercise
Express each of the following ratios in their simplest terms.
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SLIDE 4
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SLIDE 5
Express each of the following ratios as fractions in their lowest terms.
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SLIDE 6
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SLIDE 5B
Express each of the following ratios as fractions in their lowest terms.
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SLIDE 6B
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SLIDE 7
Examples
Simplify
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SLIDE 8
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SLIDE 9
Two objects are similar if their sides are in the same ratio.
State whether the following are similar or not. (The diagrams are not drawn to scale.)
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SLIDE 10
? Similar
? Similar
? Not similar
? Similar
SLIDE11
Each pair of rectangles are similar.
Find the length of the missing side.
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SLIDE 12
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SLIDE 13
In similar triangles the sides are in the same ratio
Each pair is similar. Find the missing lengths of the larger triangle. (They are not drawn to scale.)
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SLIDE 14
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SLIDE 15
Example
Divide £1200 in the ratio
Exercise
? Divide £1400 in the ratio
? Divide 120 kg in the ratio
? Divide the length 336 m in the ratio
SLIDE 16
? Divide £1400 in the ratio
? Divide 120 kg in the ratio
? Divide the length 336 m in the ratio
SLIDE 15B
Example
Divide $1200 in the ratio
Exercise
? Divide $1400 in the ratio
? Divide 120 lb in the ratio
? Divide the length 336 ft in the ratio
SLIDE 16B
? Divide $1400 in the ratio
? Divide 120 lb in the ratio
? Divide the length 336 ft in the ratio
SLIDE 17
? A sum of money is divided into two parts in the ratio . The smaller amount is £300. What is the larger amount?
? An alloy of metal comprises zinc, copper and tin in the ratio . Find the amount of the largest part in 72 kg of the alloy.
? A sum of money is divided into three parts in the ratio . If the largest share is £550, what is the total amount shared?
SLIDE 18
? A sum of money is divided into two parts in the ratio . The smaller amount is £300. What is the larger amount?
Answer: £700
? An alloy of metal comprises zinc, copper and tin in the ratio . Find the amount of the largest part in 72 kg of the alloy.
Answer: 42 kg
? A sum of money is divided into three parts in the ratio . If the largest share is £550, what is the total amount shared?
Answer: £800
SLIDE 17B
? A sum of money is divided into two parts in the ratio . The smaller amount is $300. What is the larger amount?
? An alloy of metal comprises zinc, copper and tin in the ratio . Find the amount of the largest part in 72 lb of the alloy.
? A sum of money is divided into three parts in the ratio . If the largest share is $550, what is the total amount shared?
SLIDE 18B
? A sum of money is divided into two parts in the ratio . The smaller amount is $300. What is the larger amount?
Answer: $700
? An alloy of metal comprises zinc, copper and tin in the ratio . Find the amount of the largest part in 72 lb of the alloy.
Answer: 42 lb
? A sum of money is divided into three parts in the ratio . If the largest share is $550, what is the total amount shared?
Answer: $800
SLIDE 19
In direct proportion one thing goes up in the same ratio as another. They go up in equal parts.
Example
The cost of 6 cups is £7.80. Work out the cost of 10 of these cups.
Question
To make 8 chocolate chip cookies the following are required: 80 g flour, 30 g margarine, 20 g sugar, 30 g chocolate chips, 600 ml milk. Work out how much of each ingredient will be needed to make 20 chocolate chip cookies.
SLIDE 20
To make 8 chocolate chip cookies the following are required: 80 g flour, 30 g margarine, 20 g sugar, 30 g chocolate chips, 600 ml milk. Work out how much of each ingredient will be needed to make 20 chocolate chip cookies.
200 g flour, 75 g margarine, 50 g sugar, 75 g chocolate chips, 1500 ml milk
SLIDE 19B
In direct proportion one thing goes up in the same ratio as another. They go up in equal parts.
Example
The cost of 6 cups is $7.80. Work out the cost of 10 of these cups.
Question
At a factory, to make 80 chocolate cakes the following are required: 80 oz flour, 30 oz margarine, 20 oz sugar, 30 oz chocolate chips, 60 pt milk. Work out how much of each ingredient will be needed to make 200 chocolate cakes.
SLIDE 20B
At a factory, to make 80 chocolate cakes the following are required: 80 oz flour, 30 oz margarine, 20 oz sugar, 30 oz chocolate chips, 60 pt milk. Work out how much of each ingredient will be needed to make 20 chocolate cakes.
200 oz flour, 75 oz margarine, 50 oz sugar, 75 oz chocolate chips, 150 pt milk
SLIDE 21
To make 16 biscuits the following ingredients are required: 400 g of butter, 200 g of castor sugar, 400 g of flour, 50 g of cocoa. Lynda has 1.5 kg of butter, 1.2 kg of castor sugar, 2 kg of flour and 250 g of cocoa. What is the greatest number of biscuits that Lynda can make?
SLIDE 22
To make 16 biscuits the following ingredients are required: 400 g of butter, 200 g of castor sugar, 400 g of flour, 50 g of cocoa. Lynda has 1.5 kg of butter, 1.2 kg of castor sugar, 2 kg of flour and 250 g of cocoa. What is the greatest number of biscuits that Lynda can make?
The ingredient that runs out first is the butter; with only 1.5 kg of butter, Lynda can make 3.75 times the recipe; that is, 60 biscuits.
SLIDE 21B
To make 160 biscuits the following ingredients are required: 40 oz of butter, 20 oz of castor sugar, 40 oz of flour, 5 oz of cocoa. Lynda has 150 oz of butter, 120 oz of castor sugar, 200 oz of flour and 25 oz of cocoa. What is the greatest number of biscuits that Lynda can make?
SLIDE 22B
To make 160 biscuits the following ingredients are required: 40 oz of butter, 20 oz of castor sugar, 40 oz of flour, 5 oz of cocoa. Lynda has 150 oz of butter, 120 oz of castor sugar, 200 oz of flour and 25 oz of cocoa. What is the greatest number of biscuits that Lynda can make?
The ingredient that runs out first is the butter; with only 150 oz of butter, Lynda can make 3.75 times the recipe; that is, 600 biscuits.
SLIDE 23
James and Jacob share a sum of money in the ratio . James gets £150 more than Jacob. How much money did they share altogether?
SLIDE 24
James and Jacob share a sum of money in the ratio . James gets £150 more than Jacob. How much money did they share altogether?
The sum of £150 corresponds to parts.
3 parts of the money is £150. They share £350 and get £250 and £100 respectively.
SLIDE 23B
James and Jacob share a sum of money in the ratio . James gets $150 more than Jacob. How much money did they share altogether?
SLIDE 24B
James and Jacob share a sum of money in the ratio . James gets $150 more than Jacob. How much money did they share altogether?
The sum of $150 corresponds to parts.
3 parts of the money is $150. They share $350 and get $250 and $100 respectively.
SLIDE 25
A copper pipe has a length of 60 cm and a mass of 30 g. Casmir cut a piece of this pipe that was 36 cm in length. What was the mass of the piece Casmir cut?
SLIDE 26
A copper pipe has a length of 60 cm and a mass of 30 g. Casmir cut a piece of this pipe that was 36 cm in length. What was the mass of the piece Casmir cut?
The mass is 18 g
SLIDE 25B
A copper pipe has a length of 60 in and a mass of 30 oz. Casmir cut a piece of this pipe that was 36 inches long. What was the mass of the piece Casmir cut?
SLIDE 26B
A copper pipe has a length of 60 in and a mass of 30 oz. Casmir cut a piece of this pipe that was 36 inches long. What was the mass of the piece Casmir cut?
The mass is 18 oz
SLIDE 27
A lorry uses 2 litres of fuel to 5 miles. One litre of fuel costs £1.50. What is the cost of driving the lorry 800 miles?
SLIDE 28
A lorry uses 2 litres of fuel to 5 miles. One litre of fuel costs £1.50. What is the cost of driving the lorry 800 miles?
It will cost £480
SLIDE 27B
A lorry uses 2 pt of fuel to 5 miles. One pt of fuel costs $1.50. What is the cost of driving the lorry 800 miles?
SLIDE 28B
A lorry uses 2 pt of fuel to 5 miles. One pt of fuel costs $1.50. What is the cost of driving the lorry 800 miles?
It will cost $480.
SLIDE 29
It is claimed that car A gives 34 km per litre, and that car B gives 27.5 km per litre. The driver of car A gets one fifth fewer km per litre and drives 1,500 km. The driver of car B gets three-quarters of the litres claimed and drives 1,200 km. Which driver uses more fuel?
SLIDE 30
It is claimed that car A gives 34 km per litre, and that car B gives 27.5 km per litre. The driver of car A gets one fifth fewer km per litre and drives 1,500 km. The driver of car B gets three-quarters of the litres claimed and drives 1,200 km. Which driver uses more fuel?
Car B uses more fuel.
SLIDE 29B
It is claimed that car A gives 34 miles per pint of petrol, and that car B gives 27.5 miles per pint. The driver of car A gets one fifth fewer km per litre and drives 1,500 miles. The driver of car B gets three-quarters of the litres claimed and drives 1,200 miles. Which driver uses more fuel?
SLIDE 30B
It is claimed that car A gives 34 miles per pint of petrol, and that car B gives 27.5 miles per pint. The driver of car A gets one fifth fewer km per litre and drives 1,500 miles. The driver of car B gets three-quarters of the litres claimed and drives 1,200 miles. Which driver uses more fuel?
Car B uses more fuel.
SLIDE 31
At a school there were three year groups. Year group 1 had 186 students; Year group 2 had 144 students and Year group 3 had 90 students. The school secretary took a stratified sample of 70 students by each Year group. What was the number of students in Year group 2 in her sample?
Stratified. A population may be sub-divided into distinct, separate sub-populations. For example, the population of the UK may be sub-divided by age. When this is done, the population is stratified. Here a sample indicates a small fraction of the total population.
SLIDE 32
At a school there were three year groups. Year group 1 had 186 students; Year group 2 had 144 students and Year group 3 had 90 students. The school secretary took a stratified sample of 70 students by each Year group. What was the number of students in Year group 2 in her sample?
The total number of students is 420, so the sample of 70 is 1/6 of the school. Year 1: 31, Year 2: 24, Year 3: 15
SLIDE 33
Bill donated £20,000 to three charities that help children with learning difficulties. He gave 1/5 to a charity for dyslexic children, and then divided the rest between a charity for children with dysgraphia, and a charity for children with ADD (Attention Deficit Disorder) in the ratio 3:2. How much money did Bill give to the charity for the children with dysgraphia?
SLIDE 34
Bill donated £20,000 to three charities that help children with learning difficulties. He gave 1/5 to a charity for dyslexic children, and then divided the rest between a charity for children with dysgraphia, and a charity for children with ADD (Attention Deficit Disorder) in the ratio 3:2. How much money did Bill give to the charity for the children with dysgraphia?
He gave £9,600 to the charity for dysgraphia.
SLIDE 33B
Bill donated $20,000 to three charities that help children with learning difficulties. He gave 1/5 to a charity for dyslexic children, and then divided the rest between a charity for children with dysgraphia, and a charity for children with ADD (Attention Deficit Disorder) in the ratio 3:2. How much money did Bill give to the charity for the children with dysgraphia?
SLIDE 34B
Bill donated $20,000 to three charities that help children with learning difficulties. He gave 1/5 to a charity for dyslexic children, and then divided the rest between a charity for children with dysgraphia, and a charity for children with ADD (Attention Deficit Disorder) in the ratio 3:2. How much money did Bill give to the charity for the children with dysgraphia?
He gave $9,600 to the charity for dysgraphia.
SLIDE 35
A sum of money was shared between X, Y and Z. X got 1/8 of the money; Y got 1/2 of the money; Z got the rest. If X got £2.50 how much did Y get? What was the ratio of the amount of money that Z got to the amount of money Y got? Write your answer in the form where a and b are whole numbers in their simplest ratio.
SLIDE 36
A sum of money was shared between X, Y and Z. X got 1/8 of the money; Y got 1/2 of the money; Z got the rest. If X got £2.50 how much did Y get? What was the ratio of the amount of money that Z got to the amount of money Y got? Write your answer in the form where a and b are whole numbers in their simplest ratio.
Y received £10.
SLIDE 35
A sum of money was shared between X, Y and Z. X got 1/8 of the money; Y got 1/2 of the money; Z got the rest. If X got $2.50 how much did Y get? What was the ratio of the amount of money that Z got to the amount of money Y got? Write your answer in the form where a and b are whole numbers in their simplest ratio.
SLIDE 36
A sum of money was shared between X, Y and Z. X got 1/8 of the money; Y got 1/2 of the money; Z got the rest. If X got $2.50 how much did Y get? What was the ratio of the amount of money that Z got to the amount of money Y got? Write your answer in the form where a and b are whole numbers in their simplest ratio.
Y received 410.
SLIDE 37
All percentages are fractions.
Make each of these fractions into a decimal and a percentage:
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SLIDE 38
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SLIDE 39
Convert each of these decimals into a fraction and a percentage
? 0.08 ? 0.192
Convert each of these percentages into a fraction and a decimal
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SLIDE 40
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SLIDE 41
? Calculate
(a) 40% of 60 (b) 12% of 20 (c) of 64 (d) 5% of 120.
? What percentage is
(a) 25 of 200 (b) 30 of 75 (c) 24 of 150 (d) 15 of 33?
SLIDE 42
?
(a) 40% of 60 (b) 12% of 20
(c) of 64 (d) 5% of 120
?
(a) 25 of 200 (b) 30 of 75
(c) 24 of 150 (d) 15 of 33
SLIDE 43
? A student gets 36 out of 60 in a quiz. (a) What is the student’s percentage mark? (b) If the percentage needed to pass is 45%, what is the pass mark?
? 20% of a length is 27 m. What is the complete length?
? 15% of the length of a pipe is 12 cm. What is the complete length?
SLIDE 44
? A student gets 36 out of 60 in a quiz. (a) What is the student’s percentage mark? (b) If the percentage needed to pass is 45%, what is the pass mark?
(a)
(b)
? 20% of a length is 27 m. What is the complete length?
Answer: 135 m
? 15% of the length of a pipe is 12 cm. What is the complete length?
Answer: 80 cm
SLIDE 43B
? A student gets 36 out of 60 in a quiz. (a) What is the student’s percentage mark? (b) If the percentage needed to pass is 45%, what is the pass mark?
? 20% of a length is 27 yd. What is the complete length?
? 15% of the length of a pipe is 12 in. What is the complete length?
SLIDE 44B
? A student gets 36 out of 60 in a quiz. (a) What is the student’s percentage mark? (b) If the percentage needed to pass is 45%, what is the pass mark?
(a)
(b)
? 20% of a length is 27 yd. What is the complete length?
Answer: 135 yd
? 15% of the length of a pipe is 12 in. What is the complete length?
Answer: 80 in
SLIDE 45
? 64% of a class are girls. What is the ratio of girls to boys in the class?
? The cost of a season ticket at a club was £560. The next year this was increased to £600. What was the percentage increase in the price of the season ticket?
? A ticket to a circus costs £35 plus 8% sales tax. What was the total cost of the ticket?
SLIDE 46
? 64% of a class are girls. What is the ratio of girls to boys in the class?
? The cost of a season ticket at a club was £560. The next year this was increased to £600. What was the percentage increase in the price of the season ticket?
? A ticket to a circus costs £35 plus 8% sales tax. What was the total cost of the ticket?
Answer: £37.80
SLIDE 45B
? 64% of a class are girls. What is the ratio of girls to boys in the class?
? The cost of a season ticket at a club was $560. The next year this was increased to $600. What was the percentage increase in the price of the season ticket?
? A ticket to a circus costs $35 plus 8% sales tax. What was the total cost of the ticket?
SLIDE 46B
? 64% of a class are girls. What is the ratio of girls to boys in the class?
? The cost of a season ticket at a club was $560. The next year this was increased to $600. What was the percentage increase in the price of the season ticket?
? A ticket to a circus costs $35 plus 8% sales tax. What was the total cost of the ticket?
Answer: $37.80
SLIDE 47
Reverse calculations with percentages
Sales tax on a car was 20% of its value. The price of the article after the duty had been paid was £7200. What was the price before tax?
Solution
In this question we must work backwards. We are not asked to add 20% to £7200; we are asked to find what the original price of the good was before 20% was added.
Answer: £6,000
Question
Joanna bought a washing machine. 15% sales tax was added to the price of the washing machine, after which Joanna had to pay £575. What was the price of the washing machine before the sales tax was added?
SLIDE 48
Joanna bought a washing machine. 15% sales tax was added to the price of the washing machine, after which Joanna had to pay £575. What was the price of the washing machine before the sales tax was added?
Answer: £500
SLIDE 47B
Reverse calculations with percentages
Sales tax on a car was 20% of its value. The price of the article after the duty had been paid was $7200. What was the price before tax?
Solution
In this question we must work backwards. We are not asked to add 20% to $7200; we are asked to find what the original price of the good was before 20% was added.
Answer: $6,000
Question
Joanna bought a washing machine. 15% sales tax was added to the price of the washing machine, after which Joanna had to pay $575. What was the price of the washing machine before the sales tax was added?
SLIDE 48B
Joanna bought a washing machine. 15% sales tax was added to the price of the washing machine, after which Joanna had to pay $575. What was the price of the washing machine before the sales tax was added?
Answer: $500
SLIDE 49
? The value of a car went down by 10%. After the decrease it was worth £2700. What was it worth before the decrease?
? A man sold his car for £10,200. He lost 15% of what he originally paid for it. How much did he originally pay for the car?
SLIDE 50
? The value of a car went down by 10%. After the decrease it was worth £2700. What was it worth before the decrease?
Answer: £3,000
? A man sold his car for £10,200. He lost 15% of what he originally paid for it. How much did he originally pay for the car?
Answer: £12,000
SLIDE 49B
? The value of a car went down by 10%. After the decrease it was worth $2700. What was it worth before the decrease?
? A man sold his car for $10,200. He lost 15% of what he originally paid for it. How much did he originally pay for the car?
SLIDE 50B
? The value of a car went down by 10%. After the decrease it was worth $2700. What was it worth before the decrease?
Answer: $3,000
? A man sold his car for $10,200. He lost 15% of what he originally paid for it. How much did he originally pay for the car?
Answer: $12,000
SLIDE 51
? There was an epidemic in a town, and 40% of the population caught the disease. 18,000 people did not catch the disease. How many people caught the disease?
? A company bought a printer. At the end of the year the printer had depreciated by 15% to a value of £9,350. What price did the company pay for the printer?
Depreciation = to go down in value
SLIDE 52
? There was an epidemic in a town, and 40% of the population caught the disease. 18,000 people did not catch the disease. How many people caught the disease?
Answer: 12,000
? A company bought a printer. At the end of the year the printer had depreciated by 15% to a value of £9,350. What price did the company pay for the printer?
Answer: £11,000
SLIDE 51B
? There was an epidemic in a town, and 40% of the population caught the disease. 18,000 people did not catch the disease. How many people caught the disease?
? A company bought a printer. At the end of the year the printer had depreciated by 15% to a value of $9,350. What price did the company pay for the printer?
Depreciation = to go down in value
SLIDE 52B
? There was an epidemic in a town, and 40% of the population caught the disease. 18,000 people did not catch the disease. How many people caught the disease?
Answer: 12,000
? A company bought a printer. At the end of the year the printer had depreciated by 15% to a value of $9,350. What price did the company pay for the printer?
Answer: $11,000
SLIDE 53
A traveler wishes to convert £500 to Euros.
The Bureau make a charge of 2.5% commission on the sum, and then deduct a fixed charge of £10 per transaction. After that they convert the money at the exchange rate. The exchange rate is £1 = 1.1 EUR.
Begin by deducting the 2.5% commission from £500. Then deduct the fixed charge of £10. Finally, convert the balance to euros.
SLIDE 54
Solution
Answer: 525.25 EUR
SLIDE 53B
A traveler wishes to convert $500 to Euros.
The Bureau make a charge of 2.5% commission on the sum, and then deduct a fixed charge of $10 per transaction. After that they convert the money at the exchange rate. The exchange rate is $1 = 0.85 EUR.
Begin by deducting the 2.5% commission from $500. Then deduct the fixed charge of $10. Finally, convert the balance to euros.
SLIDE 54B
Solution
SLIDE 55
The reciprocal of a number is 1 divided by that number.
The reciprocal of 2 is
Without calculator, for each of the following: (a) find as fractions the reciprocals; (b) write these fractions as decimals.
Use long division and approximation if necessary.
? 5 ? 8 ? 3
? 12 ? 16 ? 25
SLIDE 56
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SLIDE 57
The reciprocal button on the calculator
Calculators have a button for calculating the reciprocals of numbers, which they give as decimal numbers.
To use this button, you must know where it is and how it is displayed. It will be displayed as one of these
Each button on a calculator has two functions. One is displayed on the button and the other above the button. The reciprocal may be above the button. Then, to use it, you must first press the shift button. This will be a button that will have SHIFT on it or above it.
In order to use the reciprocal button, you may have to press the equals at the end. This makes the calculator complete the process.
Use the reciprocal button to find the reciprocal of each of the following. Give the answer to 4 decimal places
? 7 ? 2.351 ? 13.24
SLIDE 58
?
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?
SLIDE 59
£1 = 80 Rupee
The exchange rates of two currencies are reciprocals of each other
Question
? Convert $1200 to Pound Sterling
? Convert £350 to Dollars.
SLIDE 60
? Convert $1200 to Pound Sterling
? Convert £350 to Dollars.
SLIDE 59B
$1 = 80 Rupee
The exchange rates of two currencies are reciprocals of each other.
Question
? Convert $1200 to Pound Sterling
? Convert £350 to Dollars.
SLIDE 60B
? Convert $1200 to Pound Sterling
? Convert £350 to Dollars.
SLIDE 61
A businesswoman proposes to convert £2,000 to Chinese Yuan. The mid-market rate is £1 = 7 Yuan.
Bureau X uses the mid-market rate; it first deducts a fixed charge of £10 and then takes a commission of 5%.
Bureau Y have zero commission and quote buying and selling prices as 6 Yuan and 8 Yuan respectively.
Which bureau offers the businesswoman the better deal?
SLIDE 62
A businesswoman proposes to convert £2,000 to Chinese Yuan. The mid-market rate is £1 = 7 Yuan. Bureau X uses the mid-market rate; it first deducts a fixed charge of £10 and then takes a commission of 5%. Bureau Y have zero commission and quote buying and selling prices as 6 Yuan and 8 Yuan respectively. Which bureau offers the businesswoman the better deal?
Bureau X
Bureau Y
Bureau X offers the better deal.
SLIDE 61B
A businesswoman proposes to convert 42,000 to Chinese Yuan. The mid-market rate is 41 = 7 Yuan.
Bureau X uses the mid-market rate; it first deducts a fixed charge of 410 and then takes a commission of 5%.
Bureau Y have zero commission and quote buying and selling prices as 6 Yuan and 8 Yuan respectively.
Which bureau offers the businesswoman the better deal?
SLIDE 62B
Solution
Bureau X
Bureau Y
Bureau X offers the better deal.
SLIDE 63
Fluctuating exchange rates
A traveler goes to India. He converts £1000 to Indian rupee at a rate of £1 = 80 Rupee. But when he gets there his hosts insist on entertaining him, so he cannot spend his cash. By the time he returns to the UK the fluctuating exchange rate has altered to £1 = 90 Rupee. How much to the nearest pound sterling does the traveler lose by converting his money twice? Assume zero commission on both conversions.
To fluctuate means to change frequently in both directions, up and down, one way and the other.
SLIDE 64
A traveler goes to India. He converts £1000 to Indian rupee at a rate of £1 = 80 Rupee. But when he gets there his hosts insist on entertaining him, so he cannot spend his cash. By the time he returns to the UK the fluctuating exchange rate has altered to £1 = 90 Rupee. How much to the nearest pound sterling does the traveler lose by converting his money twice? Assume zero commission on both conversions.
Answer: he loses £111.11
SLIDE 63B
Fluctuating exchange rates
A traveler goes to India. He converts $1000 to Indian rupee at a rate of $1 = 80 Rupee. But when he gets there his hosts insist on entertaining him, so he cannot spend his cash. By the time he returns to the UK the fluctuating exchange rate has altered to £$ = 90 Rupee. How much to the nearest pound sterling does the traveler lose by converting his money twice? Assume zero commission on both conversions.
To fluctuate means to change frequently in both directions, up and down, one way and the other.
SLIDE 64B
Solution
Answer: he loses $111.11
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