Inverse Variation Using Method of Proportion
Now we will learn how to solve inverse variations using method of proportion.
We know, the two quantities may be linked in such a way that if one increases, other decreases. If one decreases, the other increases.
Some situations of inverse variation using method of proportion:
● More men at work, less time taken to finish the work.
● More speed, less time is taken to cover the same distance.
Solved examples on inverse variations using method of proportion:
1. If 63 workers can do a piece of work in 42 days, then 27 workers will complete the same work in how many days?
Solution:
This is a situation of inverse variation, now we solve using method of proportion.
Less men at work means more days are taken to complete the work.
|
Number of workers Number of Days |
63 27 42 x |
Since, the two quantities vary inversely
Therefore, 63 × 42 = 27 × x
⇒ (63 × 42)/27 = x
⇒ x = 98 days
Therefore, 27 workers can complete the same work in 98 days.
2. In a summer camp there is enough food for 250 students for 21 days. If 100 more students join the camp, how many days will the food last?
Solution:
This is a situation of inverse variation, now we solve using method of proportion.
More students means food lasts for less days.
(Here, the two quantities vary inversely)
|
Number of Students Number of Days |
250 350 21 x |
Since, the two quantities vary inversely
Therefore, 250 × 21 = 350 × x
So, x = (250 × 21)/350
⇒ x = 15 days
Therefore, for 350 students food lasts for 15 days.
3. Carol starts at 9:00 am by bicycle to reach office. She cycles at the speed of 8 km/hour and reaches the office at 9:15 am. By how much should she increase the speed so that she can reach the office at 9:10 am?
Solution:
This is a situation of inverse variation, now we solve using method of proportion.
More the speed, less will be the time taken to cover the given distance.
(Here, the two quantities vary inversely)
|
Time (in minutes) Speed (in km/hr) |
15 10 8 x |
Since, the two quantities vary inversely
Therefore, 15 × 8 = 10 × x
So, x = (15 × 8)/10
Therefore, in 10 minutes she reaches the office at the speed of 12 km/hr.
4. 25 labours can complete a work in 51 days. How many labours will complete the same work in 15 days?
Solution:
This is a situation of inverse variation, now we solve using method of proportion.
Less days, more labours at work.
(Here, the two quantities vary inversely)
|
Number of Days Number of labours |
51 15 25 x |
Since, the two quantities vary inversely
Therefore, 51 × 25 = 15 × x
So, x = (51 × 25)/15
Therefore, to complete the work in 15 days, there must be 85 labours at work.
Situations of Direct Variation
Situations of Inverse Variation
Direct Variations Using Unitary Method
Direct Variations Using Method of Proportion
Inverse Variation Using Unitary Method
Inverse Variation Using Method of Proportion
Problems on Unitary Method using Direct Variation
Problems on Unitary Method Using Inverse Variation
Mixed Problems Using Unitary Method
7th Grade Math Problems
From Inverse Variation Using Method of Proportion to HOME PAGE
Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.
Recent Articles
-
Converting Fractions to Decimals | Solved Examples | Free Worksheet
Apr 28, 25 01:43 AM
In converting fractions to decimals, we know that decimals are fractions with denominators 10, 100, 1000 etc. In order to convert other fractions into decimals, we follow the following steps: -
Expanded Form of a Number | Writing Numbers in Expanded Form | Values
Apr 27, 25 10:13 AM
We know that the number written as sum of the place-values of its digits is called the expanded form of a number. In expanded form of a number, the number is shown according to the place values of its… -
Converting Decimals to Fractions | Solved Examples | Free Worksheet
Apr 26, 25 04:56 PM
In converting decimals to fractions, we know that a decimal can always be converted into a fraction by using the following steps: Step I: Obtain the decimal. Step II: Remove the decimal points from th… -
Worksheet on Decimal Numbers | Decimals Number Concepts | Answers
Apr 26, 25 03:48 PM
Practice different types of math questions given in the worksheet on decimal numbers, these math problems will help the students to review decimals number concepts. -
Multiplication Table of 4 |Read and Write the Table of 4|4 Times Table
Apr 26, 25 01:00 PM
Repeated addition by 4’s means the multiplication table of 4. (i) When 5 candle-stands having four candles each. By repeated addition we can show 4 + 4 + 4 + 4 + 4 = 20 Then, four 5 times
Worksheet on Direct Variation using Unitary Method
Worksheet on Direct variation using Method of Proportion
Worksheet on Word Problems on Unitary Method
Worksheet on Inverse Variation Using Unitary Method
New! Comments
Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.