"Question 10 Two persons could fit new windows in house in 3 days. (i) One of the persons fell ill before the work started. How long would the job take now? (ii) How many persons would be needed to fit the windows in one day?
Class 8 Direct and Inverse Proportions Page 214"
Answers
Inverse variation:
Two quantities x and y are said to vary inversely or indirectly if an increase in x causes a decrease in y and a decrease in X causes an increase in y in such a way that xy remains constant.
In other words x and y are said to vary indirectly if x y = k, where K is a positive constant.
In inverse Proportion
xy= k
x=k/y
So we can find value of k from known values, and then use the formula to calculate the unknown values
When two quantities x and y are in direct proportion (or vary directly) they are also written as x∝y.
When two quantities x and y are in inverse proportion (or vary inversely) they are also written as x∝ 1/y
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Solution:
Table is in the attachment
(i) Let the number of days required by 1 man to fit all the windows be x.
Less the number of persons, more will be the number of days required to fit all the windows.
Hence, this is a case of inverse proportion.
2 × 3 = 1× x
x = 6
Hence, the number of days taken by 1 man to fit all the windows is 6.
(ii) Let the number of persons required to fit all the windows in one day be y.
Less the number of days, more will be the number of persons required to fit all the windows.
Hence, this is a case of inverse proportion.
2 × 3 = y × 1
y = 6
Hence, 6 persons are required to fit all the windows in one day.
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Hope this will help you....
Answer:
6 person can fit the windows in one day