Question

What is the method to solve inverse proportion

Answer 1

Examples:
1) The time taken to finish a work varies inversely as the number of people doing the work. (More number of people, less time; Less number of people, more time)
2) Time taken to cover a distance varies inversely with speed. (More the speed, less the time; Less the speed more time).
In general if a and b are inversely proportional, then their product $a\times b$ is always a constant.
Worked example :
If 35 men take 20 days to reap a field, in how many days can 20 men reap the field.
1 man will need $(35\times 20)$ days to reap the field = 700 days. (Less men, more days)
20 men will need \rightarrow $\frac{700}{20}=35$ days. (Now 20 men are there which is more than 1 man, hence time taken is less)
In other way,
$a_1\times b_1=a_2\times b_2$
$a_1=35$ men, $b_1=20$ days, $a_2=20$ men, $b_2=??$
$\to 35\times 20=20\times ??$
??$=\frac{35\times 20}{20}=35days$
Answer : 35 days.