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
-
5th Grade Highest Common Factor | HCF | GCD|Prime Factorization Method
Mar 24, 25 03:40 PM
The highest common factor (H.C.F.) of two or more numbers is the highest or greatest common number or divisor which divides each given number exactly. Hence, it is also called Greatest Common Divisor… -
5th Grade Factors and Multiples | Definitions | Solved Examples | Math
Mar 23, 25 02:39 PM
Here we will discuss how factors and multiples are related to each other in math. A factor of a number is a divisor which divides the dividend exactly. A factor of a number which is a prime number is… -
Adding 2-Digit Numbers | Add Two Two-Digit Numbers without Carrying
Mar 23, 25 12:43 PM
Here we will learn adding 2-digit numbers without regrouping and start working with easy numbers to get acquainted with the addition of two numbers. -
Worksheet on 12 Times Table | Printable Multiplication Table | Video
Mar 23, 25 10:28 AM
Worksheet on 12 times table can be printed out. Homeschoolers can also use these multiplication table sheets to practice at home. -
Vertical Subtraction | Examples | Word Problems| Video |Column Method
Mar 22, 25 05:20 PM
Vertical subtraction of 1-digit number are done by arranging the numbers column wise i.e., one number under the other number. How to subtract 1-digit number vertically?
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.