# Basic Math MCQ 13 (Men and Women and a wall construction days)

MCQ 13: If 3 men or 4 women can construct a wall in 43 days, then the number of days that 7 men and 5 women take to construct it is :

a)  12 days                      b) 14 days                             c) 16 days                     d) 18 days

Solution:

Let’s suppose;

Men =M

Women=W

By given statement, work by 3 men or 4 women is eqaul; i-e

3M=4W  ==>    ​$$W=\frac{7}{5}M$$​ —————(1)

Then   7 men  and 5 women are;

$7 M + 5 W =7M+\frac{3}{4}M=\frac{31}{4}M$

So work of 7 men and 5 women are equal to ​​$$\frac{31}{4}Men$$

Now we consider only men;

Data for men can be arranged as;

 Men Days 3 43 31/4 =7.75 x

There is inverse proportion between men and days i-e more men less days wil be required to finish the work!

$\frac{x}{43}=\frac{3}{7.75}$ = 16 days aprox

So  7 men and 5 women will finish the wrok in 16 days — option c is correct

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