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Exercise 4 - Example 		Home
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Tom travelled 60 miles in 1 hour and 120 miles in 2 hours.
The ratio of time is 1 hour to 2 hour = 1:2
The ratio of distance is 60 miles to 120 miles = 60:120
1:2 and 60:120 are equivalent ratios.
1:2 = 60:120 (or) 1:2 :: 60:120 (or) 1/2 = 60/120
A proportion can be written as = or ::
In 1:2 :: 60:120 ==> 1 and 120 are EXTREMES & 2 and 60 are MEANS.
IN A PROPORTION, PRODUCT OF EXTREMES (1 X 120 = 120) = PRODUCT OF MEANS (2 X 60 =120).
To test for proportion either use equal ratio or cross product.
1. Is 2:12 = 5:30 a proportion.
2/12 = 5/30 check for cross products (products of extremes and means).
2 x 30 = 60 & 5 x 12 = 60
60 = 60 hence 2:12 = 5:30 is a proportion.

2. Find the value of y in: 1:9 = y:54
1/9 = y/54
1 x 54 = y x 9
54 = y x 9
54/9 = y
6 = y

3. The ratio of father to son age is 5:1, if dad is 40 years old, how old is the son?
(Father age is 5 parts and Son age is 1 part. 5 parts = 40 ==> 1 part = 40/5 = 8)
5:1 = 40:X
5/1 = 40/X
X = 40 x 1/5 = 8
8 years old.

4. The ratio of father to son income is 5:2, if the total income is 14,000 dollars, find their individual income?
Father income is 5 parts and Son income is 2 parts. Total = 5 + 2 = 7 parts
7 parts = 14,000
1 part = 2,000
Father income = 5 parts = 5 x 2000 = 10,000 dollars
Son income = 2 parts = 2 x 2000 = 4,000 dollars

1. Convert fraction 3/20 to percent:
Method 1: Write equivalent fraction to 3/20 with denominator 100. The equivalent fraction is percent.
3/20 = 15/100 = 15%

Method 2: Write 144/200 in percentage
144/200 of 100 = (144 x 100)/200 = 72%

Write 7/9 in percentage
7/9 of 100 = (7 x 100)/9 = 77 7/9%

2. Convert 17 1/2% to fraction:
17 1/2% = 35/2 x 1/100 = 35/200 = 7/40

3. Find 12 1/2% of 40:
12 1/2% = 25/2 x 1/100 = 25/200 = 1/8
1/8 of 40 = 1/8 x 40 = 5

4. Find value of X in: 6 1/4% of X = 100
6 1/4% = 25/4 x 1/100 = 25/400 = 1/16
1/16 of X = 100
X = 100 x 16/1
X = 1600

5. Find the value of A: A % of 800 = 144
A/100 of 800 = 144
A/100 x 800 = 144
A = 144/800 x 100
A = 18
A% = 18%

Simple Interest:
If you deposit $1000 in a bank for one year, the bank pays an Interest of $5. The interest paid for $1000 for 1 year is called the rate of interest (I).

Similarly, when money is borrowed from a bank, at the end of a specified time period, interest on the money borrowed need to be paid. The amount of money borrowed is called principal (p).

The total amount (the principal + interest ) of money is called the amount (A).
Amount = Principal + Interest
A = p + I
Simple Interest, I = pnr/100
If amount is given, A = p[1 + nr/100]
Where, p is the principal, r is the rate of interest per annum (per year) and n the number of years.

Example 1: Jane borrowed $4000 for 8% simple interest per annum. What is the simple interest she will pay for 4 years. What is the amount she need to pay to close the loan after 4 years?
p = $4000, r = 8%, n = 4years
I = pnr/100 = (4000 x 4 x 8)/100 = $1280
Amount (after 4 years to close the loan) = Principal + Interest = $4000 + $1280 = $5280

Principal, p = (100 x I)/nr Number of years, n = (100 x I)/pr Rate of interest, r = (100 x I)/np
Example 2: Jane deposited some amount in the bank for 5% simple interest per annum for 2 years. If the simple interest is $50, calculate the principal.
I = $50, r = 5%, n = 2years
p = (100 x I)/nr = (100 x 50)/(5 x 2) = $500


Example 3: Find the simple interest and amount on $3000 for 150 days at 4 1/2 % per annum. P = $3000, n = 150 days = 150/365 years
r = 4 1/2 % = 9/2 %
S.I = Pnr/100 = (3000) x (150/360) x (9/2) x (1/100) = $56.25
Amount = 3000 + 56.25 = $3056.25

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