Question : If 2 men or 4 women can build a wall in 34 days, in how many days can 6 men and 5 women build the same wall?
Option 1: 24
Option 2: 8
Option 3: 12
Option 4: 16
Correct Answer: 8
Solution :
If 2 men can build the wall in 34 days, then 1 man can build it in 2 × 34 days
⇒ work rate of 1 man = $\frac{ 1}{2×34}$ per day
if 4 women can build the wall in 34 days, then 1 woman can build it in 4 × 34 days.
⇒ work rate of 1 women = $\frac{1}{4 × 34}$ per day
Now, 6 men and 5 women working together
⇒ Combined work = 6 × $\frac{ 1}{2×34}$ + 5 × $\frac{1}{4 × 34}$ = $\frac{6}{68}$ + $\frac{5}{136}$ = $\frac{17}{136}$
Now,
Number of days required = $\frac{1}{\text{Combined work rate}}$ = $\frac{1}{\frac{17}{136}}$ = $\frac{136}{17}$ = 8
Hence, the correct answer is 8
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