Question

If 72 men can build a wall 280m long in 21 days, how many men will take 18 days to build a similar type of wall of length 100m?

Answer 1

Hint: To find the number of men that could take 18 days to build a similar type of wall of length 100 m, first we will determine that the number of men required to build a wall is directly proportional to length and inversely proportional to the time i.e. $ m\times \dfrac{t}{l}=\text{constant} $ . Then we will find the number of men by equalizing both the situations by taking $ {{m}_{1}}\times \dfrac{{{t}_{1}}}{{{l}_{1}}}={{m}_{2}}\times \dfrac{{{t}_{2}}}{{{l}_{2}}} $ .

Complete step-by-step answer:
According to the question, we know that the number of men required to build a wall increases with increasing length of the wall and it decreases with increasing time given for building the wall.
So, we determine that the number of men required to build a wall, is directly proportional to the length of the wall and it is inversely proportional to the time required for building the wall. So we have the following condition –
 $ \Rightarrow m\times \dfrac{t}{l}=\text{constant} $ ……………….. (1)
Where, $ \text{m=men, l=length and t=time} $ .
 According to the info given in question, we have –
If 72 men can build a wall of 280 m length in 21 days, let us consider ‘n’ denotes the number of men that could take 18 days to build a similar type of wall of length 100 m.
Therefore, by applying condition (1) to the above mentioned data, we get the following relation –
 $ {{m}_{1}}\times \dfrac{{{t}_{1}}}{{{l}_{1}}}={{m}_{2}}\times \dfrac{{{t}_{2}}}{{{l}_{2}}} $
 $ \Rightarrow n\times \dfrac{18}{100}=72\times \dfrac{21}{280} $ (Where, $ {{m}_{1}}=n,{{t}_{1}}=18,{{l}_{1}}=100,{{m}_{2}}=72,{{t}_{2}}=21\And {{l}_{2}}=280 $ )
 By cancelling common factors from numerator and denominator on both sides, we get –
 $ \Rightarrow \dfrac{9n}{50}=9\times \dfrac{3}{5} $
By simplifying the above equation, we get –
 $ \Rightarrow \dfrac{9n}{50}=\dfrac{27}{5} $
By multiplying both sides with 50, we get –
 $ \Rightarrow 9n=\dfrac{27}{5}\times 50 $
By cancelling the common factors from numerator and denominator, we get –
 $ \Rightarrow 9n=270 $
By dividing both sides by 9, we get –
 $ n=\dfrac{270}{9} $
By cancelling common factors from numerator and denominator, we get –
 $ n=30 $
Hence, number of men that could take 18 days to build a similar type of wall of length 100 m is 30 men

Note: Students get confused and can misunderstand the question. As it is given that both the walls are of the same type, they may misunderstand and take it as the length of both the walls are equal which may lead them to get the wrong answer. They should read the question carefully so as to solve the answer correctly.