RATIO AND PROPORTION PROBLEMS
Problem 1 :
If there are two lengths such that a = 90 cm and b = 120 cm, then find the ratio between them.
Solution :
a : b = 90 : 120
a : b = 3 : 4
Hence, the ratio between the two lengths is
3 to 4
From question no. 2 to question no.8, please use the information in the table given below.
Problem 2 :
Find the ratio of the age of John to David.
Solution :
Age of John = 17 years
Age of David = 15 years
Age of John : Age of David = 17 : 15
Hence, the ratio of the age of John to David is
17 to 15
Problem 3 :
Find the ratio of the age of David to John.
Solution :
Age of David = 15 years
Age of John = 17 years
Age of David : Age of John = 15 : 17
Hence, the ratio of the age of David to John is
15 to 17
Problem 4 :
Find the ratio of the weight of David to John.
Solution :
Weight of David = 29 kg
Weight of John = 31 kg
Weight of David : Weight of John = 29 : 31
Hence, the ratio of the Weight of David to John is
29 to 31
Problem 5 :
Find the ratio of the height of John to David.
Solution :
Height of John is
= 1m + 36cm
= 100cm + 36cm
= 136 cm
Height of David = 123 cm
Height of John : Height of David = 136 : 123
Hence, the ratio of the height of John to height of David is
136 to 123
Problem 6 :
Find the ratio of studying time of John to David.
Solution :
Studying time of John is
= 4 hours
= 4 ⋅ 60 min
= 240 minutes
Studying time of David = 180 minutes
Studying time --> John : David = 240 : 180
Studying time --> John : David = 4 : 3
Hence, the ratio of studying time of John to David is
4 to 3
Problem 7 :
Find the ratio of speed of cycling between John and David.
Solution :
Speed of cycling of John = 10 kmph
Speed of cycling of David = 15 kmph
Speed of cycling --> John : David = 10 : 15
Speed of cycling --> John : David = 2 : 3
Hence, the ratio of speed of cycling between John and David is
2 to 3
Problem 8 :
Find the ratio of playing time of John to David.
Solution :
Playing time of John = 2 hours
Playing time of David = 1 hour
Playing time --> John : David = 2 : 1
Hence, the ratio of playing time of John to David is
2 to 1
Problem 9 :
A student has 12 note books and 8 text books. Find the ratio of the note books to text books.
Solution :
No. of note books = 12
No. of textbooks = 8
No. of note books : No. of textbooks = 12 : 8
No. of note books : No. of textbooks = 3 : 2
Hence, the ratio of notebooks to textbooks is
3 to 2
Problem 10 :
The cost of a pen is $3 and the cost of pencil is $1.50. Find the ratio of the cost of a pen to pencil.
Solution :
Cost of a pen = $3 = 3 ⋅ 100 = 300 pennies
Cost of a pencil = $1.50 = 1.50 ⋅ 100 = 150 pennies
Cost of a pen : Cost of a pencil = 300 : 150
Cost of a pen : Cost of a pencil = 2 : 1
Hence, the ratio of cost of a pen to pencil is
2 to 1
(From problem no. 11 to problem no.13, please use the information given below)
In a Village of 10,000 people, 4,000 are Government Employees and the remaining are self-employed.
Problem 11 :
Find the ratio of the government employees to people of the village.
Solution :
No. of government employees = 4000
Total no. of people in the village = 10000
Government employees : Village people = 4000 : 10000
= 2 : 5
Hence, the ratio of government employees to village people is
2 to 5
Problem 12 :
Find the ratio of self employed to people of the village.
Solution :
No. of self employed is
= 10000 - 4000
= 6000
Total no. of people in the village = 10000
Self employed : Village people = 6000 : 10000
= 3 : 5
Hence, the ratio of self employed to village people is
3 to 5
Problem 13 :
Find the ratio of self employed to government employees.
Solution :
No. of self employed is
= 10000 - 4000
= 6000
No. of government employees = 4000
Self employed : Government employees = 6000 : 4000
Self employed : Government employees = 3 : 2
Hence, the ratio of self employed to government employees is
3 to 2
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WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Trigonometry word problems
Markup and markdown word problems
Word problems on mixed fractrions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
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