Two men and three women completed only one fourth portion of a job in 3 days. After 3 days, another man was included in the team and two days they completed another one fourth portion of the job. How many men (with no women) can complete the whole job in 4 days? (Work & Time)

প্রশ্নে বলা হচ্ছে, 2 জন পুরুষ এবং 3 জন নারী 3 দিনে একটি কাজের $\frac{1}{4}$ অংশ করতে পারে। 3 দিন পরে ঐ দলে আরেকজন পুরুষ যোগ দিলে 2 দিনে তারা কাজের আরো $\frac{1}{4}$ অংশ শেষ করলো। কতজন পুরুষ 4 দিনে ঐ কাজটি শেষ করতে পারবে?

2 man + 3 women, in 3 days complete $\frac{1}{4}$ Portion

∴ 2 man + 3 women, in 1 days complete $= \frac{1}{4 \times 3} = \frac{1}{2}$ Portion

∴ Now, 3 men + 3 women, in 2 days complete $= \frac{1}{4}$ Portion

∴ 3 men + 3 women, in 1 days complete $= \frac{1}{4 \times 2} = \frac{1}{8}$ Portion

∴ 1 man can complete in 1 day $= \left(\frac{1}{8}- \frac{1}{12}\right) = \frac{3-2}{24}= \frac{1}{24}$ Portion of the work.

Now, $\frac{1}{24}$ portion of the work is done in 1 day by 1 man

∴  1 (Complete) portion of the work is done in 1 day by $= \frac{24 \times 1}{1}$ man

∴  1 (Complete) portion of the work is done in 4 day by $= \frac{24 \times 1}{4 \times 1} = 6$  men