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
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