Question

20 men or 24 women can complete a piece of work in 20 days. If 30 men and 12 women under take to complete the work, the work will be complete in

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Answer 1

$<b><u>Given :-</u></b>$

20 men or 24 women can complete a piece of work in 20 days.

$\rule {330}{5}$

$<b><u>To Find :-</u></b>$

Number of days taken by 30 men and 12 women to complete the work.

$\rule {330}{5}$

$<b><u>Solution :-</u></b>$

$<b><u>Method (1) :</u></b>$

⇒20 men = 24 women

⇒1 man = $\frac{24}{20}$ women

•°• 1 man = $\frac{6}{5}$women

⇒30 men = $\frac{6}{5}$ × 30 women

•°• 30 men = 36 women

•°• 30 men + 12 women = 36 + 12

= 48 women

Now, M₁ = 24, M₂ = 48, W₁ = W₂ = 1, D₁ = 20 and D₂ = ?

$<b><u>According to the formula</u></b>$

M₁ × D₁ × W₂ = M₂ × D₂ × W₁

⇒ 24 × 20 × 1 = 48 × D₂ × 1

⇒ D₂ = $\frac{24\:×\:20}{48}$

⇒ D₂ = 10 days

$<b>•°• Number of days taken by 30 men and 12 women to complete the work = 10 days </b>$

$\rule {330}{5}$

$<b><u>Method (2) :</u></b>$

If a₁ men or b₁ women can finish a work in D days, then time taken by a₂ men and b₂ women to complete the work = $\frac{D(a₁b₁}{(a₂b₁ + a₁b₂}$ days

Here, a₁ = 20, b₁ = 24, a₂ = 30, b₂ = 12 and D = 20

•°• Number of days = $\frac{D(a₁b₁)}{(a₂b₁ + a₁b₂}$ days

= $\frac{20(20 × 24)}{(30 × 24 + 20 × 12}$

= $\frac{9600}{960}$ days

= 10 days

$<b>•°• Number of days taken by 30 men and 12 women to complete the work = 10 days </b>$

Answer 2

Answer:

10 Days

Step-by-step explanation:

20 M = 20 Days, 24W=20 Days

30M+12W= x days

soln:

x= 20/ ( (30/20) +(12/24) )

= 20/ ( (3/2)+(1/2))

= 20 / ( 1.5+0.5 )

= 20/2

x= 10 days