Question

A wall of 100 meters can be built by 7 men or 10 women in 10 days.How many days will 14
men and 20 women take to build a wall of 600 meters?
$a)15$
 $b)20$
 $c)25$
 $d)30$

Answer 1

Hint: First we have to know the wall built by one man or one woman per each day.After that wall built by 14 men and 20 women of 600 meters. Here “14 men and 20 women” represent both men and women together building the wall of 600 meters.So we have to include both women and men.

Complete step by step answer:
From the problem, we have given that,
A wall can be built by 7 men in 10 days = $100m$
A wall can be built by 7 men in 1 day = $\dfrac{100}{10}$=$10m$ per day
Whereas,a wall created by 7×2=14 men in one day =$10\times 2m$=$20m$
Similarly,
A wall created by 10 women in 10 days = $100m$.
A wall created by 10 women in 1 day = $\dfrac{100}{10}$=$10m$ per day
Whereas,a wall created by 10×2=20 women in 1 day = $10\times 2m$=$20m$
Therefore, the wall created by 14 men and 20 women in 1 day = $20m$+$20m$=$40m$
Here for 40 meters, it takes 1 day
So the number of days required to complete 600m = $\dfrac{600}{40}$ = 15 days
Hence, the number of days will take for 14 men and 20 women of 600m will be completed in 15 days.
The correct option is (a)

Note:
The above problem can also be solved in an alternative method by using ratio proportions as
 follows,
Alternative Method:
Consider, the required number of days =
 “7 men or 10 women” represents 7men = 10 women
14 men and 20 women = 20+20=40 women
More length of the wall means, more number of days(Direct proportion)
More women, less number of days(Indirect proportion)
\[\begin{align}
  & Length\to 100:600 \\
 & Women\to 40:10 \\
\end{align}\] ∷ 10 :$x$
∴$x$=$\dfrac{600\times 10\times 10}{100\times 40}$
   $x$=15 days