Question

If 3 man and 4 women finish their work in 8 days and 5 man and 6 women finish their work in 5 days. Find that only 1 man will take how many days.

I will follow you and give 20 points and will mark your answer as brainliest.

Answer 1

Gɪᴠᴇɴ :-

• 3 man and 4 women finish their work in 8 days.
• 5 man and 6 women finish their work in 5 days.

Tᴏ Fɪɴᴅ :-

• Find that only 1 man will take how many days. ?

Sᴏʟᴜᴛɪᴏɴ :-

since work is same in Both case ,

→ 8(3M + 4W) = 5(5M + 6W)

→ 24M + 32W = 25M + 30W

→ 25M - 24M = 32W - 30W

→ M = 2W

→ (M/W) = (2/1)

So, Efficiency of M : W = 2 : 1 .

Therefore ,,

→ Total work = 8(3*2 + 4*1) = 8(6 + 4) = 8*10 = 80 units.

Hence,

→ Total work done by 1 Man alone in = (80/2) = 40 Days. (Ans.)

∴ Only 1 Man will take 40 Days to complete the whole work.

Answer 2

$\huge \tt \underline \orange {Answer}$

$\huge \bf \pink{Given,}$

$\huge \sf \blue{3 \: M + 4 \: W =8 \: day }$

$\huge \sf \blue{5\: M + 6 \: W =5\: day }$

$\rm \green{ \frac{3}{m} + \frac{4}{m} = \frac{1}{8} }$

$\rm \green{ 3w + 4m = \frac{mw}{8} }$

$\rm \green{ 24 \: w + 32 \: m = mv }$

$\bf \orange{ w = 2 \: m \: \: \: \: \: \: \: \: \: \: \: w - 2 \: m \: = 0 }$

$\bf \green{ \frac{5}{m} + \frac{6}{w} = \frac{1}{5} }$

$\bf \green{ 5 \: w + 6 \: m = \frac{mw}{5} }$

$\bf \green{ 25 \: w + 30 \: m = mw }$

$\bf\red{ \frac{3}{m} + \frac{4}{2m} = \frac{1}{8} }$

$\bf\red{ \implies \frac{3}{m} + \frac{2}{m} = \frac{1}{8} }$

$\bf\red{ \implies \frac{5}{m} = \frac{1}{8} }$

${ \huge{ \boxed{ \tt \pink{Therefore, 40 \: Men}}}}$