Introduction to proportion questions:
Algebra is with the purpose of separation of mathematics in which calculation are made by using any arbitrary characters to stand for the quantities or things considered. In our day-to-day life, by learning ratio and proportion many a times we compare two quantities of the same type. Thus, in convinced situations, comparisons by division make better sense than comparison by taking the difference. The comparison by division is the Ratio. We denote ratio-using symbol ‘:’. If two ratios are the same, we state that they are in proportion and use the symbol ‘:’ or ‘=’ to equate the two ratios.In this article, we are going to discuss about proportion questions.
Proportion Questions – Definition and Types:
Definition of proposition:
If two ratios are not equal, then we state that they are not in proportion. In a statement of learning proposition, the four quantities involved when taken in order are known as respective terms. First and fourth terms are known as extreme terms. Second and third terms are known as middle terms.
a: b = c : d
There are two types of propositions,
1. Simple proposition:
A proposition consisting of just individual subject and one predicate is called a simple proposition.
Example: The following are simple proposition
1. Ram is blind.
2. The flower is not red.
2. Compound proposition
A proposition consisting of two or further simple propositions in the form of a single sentence is called a compound proposition.Is this topic free online math tutor hard for you? Watch out for my coming posts.
Example: The following are compound propositions,
Quadrilateral is a square and each side of this quadrilateral is 4cm long.
Proportion Questions – Example Problems:
Question 1:
The income and savings of a family are in the ratio 6: 4. If the income of the family is Rs.7, 500. Find how much is being saved.
Solution:
Let the savings be Rs. m.
The proportion is 6: 4 = 7500: m
(Income: Saving) = (Income: Saving)
`6m = 4 xx 7500`
`(6m) / 6 = (4 xx 7500) / 6`
`m = 30000 / 5`
`m = 6000`
The Savings = Rs.6000 .
Question 2:
Jack works as a dental hygienist. Last week, Jack made `$` 720 for 36 hours of work. How many hours must Jack work in order to make `$` 950?
Solution:
Jack works as a dental hygienist
`($720) / (36hours)` = `($950) / (y hours)`
`(36 hours) xx ($950)` = `(y hours) xx ($720)`
34200 = $720 y
`(34200) / (720)` = y
47.5 = x
Jack 47 hours 5 mins work in order to make $950
Question 3:
If the cost of 11m rope is Rs. 80, find the cost of 6m cloth.
Quantity(in m) Cost (in Rs.)
11 96
6 ?
Solution:
The proportion is
11: 6 = 96: ?
Product of means = `6 xx 96` = 576
Product of Extremes = `11 xx k`
`11 xx k = 576`
`(11 xx k) / 11` = `576 / 11`
k = `576 / 11`
`k = 52.36 `
The cost of 6 m cloth = Rs. `52.36`
Algebra is with the purpose of separation of mathematics in which calculation are made by using any arbitrary characters to stand for the quantities or things considered. In our day-to-day life, by learning ratio and proportion many a times we compare two quantities of the same type. Thus, in convinced situations, comparisons by division make better sense than comparison by taking the difference. The comparison by division is the Ratio. We denote ratio-using symbol ‘:’. If two ratios are the same, we state that they are in proportion and use the symbol ‘:’ or ‘=’ to equate the two ratios.In this article, we are going to discuss about proportion questions.
Proportion Questions – Definition and Types:
Definition of proposition:
If two ratios are not equal, then we state that they are not in proportion. In a statement of learning proposition, the four quantities involved when taken in order are known as respective terms. First and fourth terms are known as extreme terms. Second and third terms are known as middle terms.
a: b = c : d
There are two types of propositions,
1. Simple proposition:
A proposition consisting of just individual subject and one predicate is called a simple proposition.
Example: The following are simple proposition
1. Ram is blind.
2. The flower is not red.
2. Compound proposition
A proposition consisting of two or further simple propositions in the form of a single sentence is called a compound proposition.Is this topic free online math tutor hard for you? Watch out for my coming posts.
Example: The following are compound propositions,
Quadrilateral is a square and each side of this quadrilateral is 4cm long.
Proportion Questions – Example Problems:
Question 1:
The income and savings of a family are in the ratio 6: 4. If the income of the family is Rs.7, 500. Find how much is being saved.
Solution:
Let the savings be Rs. m.
The proportion is 6: 4 = 7500: m
(Income: Saving) = (Income: Saving)
`6m = 4 xx 7500`
`(6m) / 6 = (4 xx 7500) / 6`
`m = 30000 / 5`
`m = 6000`
The Savings = Rs.6000 .
Question 2:
Jack works as a dental hygienist. Last week, Jack made `$` 720 for 36 hours of work. How many hours must Jack work in order to make `$` 950?
Solution:
Jack works as a dental hygienist
`($720) / (36hours)` = `($950) / (y hours)`
`(36 hours) xx ($950)` = `(y hours) xx ($720)`
34200 = $720 y
`(34200) / (720)` = y
47.5 = x
Jack 47 hours 5 mins work in order to make $950
Question 3:
If the cost of 11m rope is Rs. 80, find the cost of 6m cloth.
Quantity(in m) Cost (in Rs.)
11 96
6 ?
Solution:
The proportion is
11: 6 = 96: ?
Product of means = `6 xx 96` = 576
Product of Extremes = `11 xx k`
`11 xx k = 576`
`(11 xx k) / 11` = `576 / 11`
k = `576 / 11`
`k = 52.36 `
The cost of 6 m cloth = Rs. `52.36`
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