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3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to finish the work ?

120 days
210 days
34 days
415 days

Answer:- 1

Explanation:-

Solution:

According to the question,
As they complete the same work in same time
6 men + 5 women
= 6 men + 3 men
= 9 men
If, 3 men does a work in 12 days
1 men does a work in 12 × 3
9 men does a work in

\frac{12 \times 3}{9}

$\frac{{{\text{12}} \times {\text{3}}}}{9}$ = 4 days

Alternate :

\begin{aligned} 3 men \times 12 = 5 women \times 12 \\ \frac{men}{women} = \frac{5}{3} \\ Total work \\ = 3 \times 5 \times 12 \\ = 15 \times 12 \\ = 180 units \\ Efficiency of 6 men + 5 women \\ = 6 \times 5 + 5 \times 3 \\ = 45 \\ Time taken by 6 men + 5 women \\ = \frac{180}{45} \\ = 4 days \end{aligned}

$\eqalign{ & 3{\text{ men}} \times {\text{12}} = {\text{5 women}} \times {\text{12}} \cr & \frac{{{\text{men}}}}{{{\text{women}}}} = \frac{5}{3} \cr & {\text{Total work}} \cr & = 3 \times 5 \times 12 \cr & = 15 \times 12 \cr & = 180{\text{ units}} \cr & {\text{Efficiency of 6 men}} + {\text{5 women}} \cr & = 6 \times 5 + 5 \times 3 \cr & = 45 \cr & {\text{Time taken by 6 men}} + {\text{5 women}} \cr & = \frac{{180}}{{45}} \cr & = 4{\text{ days}} \cr}$

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= 4 days

Alternate :

\begin{aligned} 3 men \times 12 = 5 women \times 12 \\ \frac{men}{women} = \frac{5}{3} \\ Total work \\ = 3 \times 5 \times 12 \\ = 15 \times 12 \\ = 180 units \\ Efficiency of 6 men + 5 women \\ = 6 \times 5 + 5 \times 3 \\ = 45 \\ Time taken by 6 men + 5 women \\ = \frac{180}{45} \\ = 4 days \end{aligned}

$\eqalign{ & 3{\text{ men}} \times {\text{12}} = {\text{5 women}} \times {\text{12}} \cr & \frac{{{\text{men}}}}{{{\text{women}}}} = \frac{5}{3} \cr & {\text{Total work}} \cr & = 3 \times 5 \times 12 \cr & = 15 \times 12 \cr & = 180{\text{ units}} \cr & {\text{Efficiency of 6 men}} + {\text{5 women}} \cr & = 6 \times 5 + 5 \times 3 \cr & = 45 \cr & {\text{Time taken by 6 men}} + {\text{5 women}} \cr & = \frac{{180}}{{45}} \cr & = 4{\text{ days}} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

According to the question,
As they complete the same work in same time
6 men + 5 women
= 6 men + 3 men
= 9 men
If, 3 men does a work in 12 days
1 men does a work in 12 × 3
9 men does a work in

\frac{12 \times 3}{9}

$\frac{{{\text{12}} \times {\text{3}}}}{9}$ = 4 days

Alternate :

\begin{aligned} 3 men \times 12 = 5 women \times 12 \\ \frac{men}{women} = \frac{5}{3} \\ Total work \\ = 3 \times 5 \times 12 \\ = 15 \times 12 \\ = 180 units \\ Efficiency of 6 men + 5 women \\ = 6 \times 5 + 5 \times 3 \\ = 45 \\ Time taken by 6 men + 5 women \\ = \frac{180}{45} \\ = 4 days \end{aligned}

$\eqalign{ & 3{\text{ men}} \times {\text{12}} = {\text{5 women}} \times {\text{12}} \cr & \frac{{{\text{men}}}}{{{\text{women}}}} = \frac{5}{3} \cr & {\text{Total work}} \cr & = 3 \times 5 \times 12 \cr & = 15 \times 12 \cr & = 180{\text{ units}} \cr & {\text{Efficiency of 6 men}} + {\text{5 women}} \cr & = 6 \times 5 + 5 \times 3 \cr & = 45 \cr & {\text{Time taken by 6 men}} + {\text{5 women}} \cr & = \frac{{180}}{{45}} \cr & = 4{\text{ days}} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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