Twenty four men can complete a work in sixteen days. Thirty two women

1.	Twenty four men can complete a work in sixteen days. Thirty two women can complete the same work in twenty four days. Sixteen men and sixteen women started working and worked for 12 days. How many more men are to be added to complete the remaining work in 2 days ? (a) 16 (b) 24 (c) 36 (d) 48
Answer» (b) 24 1 man’s 1 days’ work = \(\frac{1}{24\times16}\) \(\therefore\) 16 men’s 1days’ work = \(\frac{16}{24\times16}\) = \(\frac{1}{24}\) 1 woman’s 1 days’ work = \(\frac{1}{32\times24}\) 16 women’s 1 days’ work = \(\frac{16}{32\times24}\) = \(\frac{1}{48}\) \(\therefore\) 12 days’ work of (16 men + 16 women) = 12\(\big(\frac{1}{24}+\frac{1}{48}\big)\) = 12\(\big(\frac{2+1}{48}\big)\) = 12 x \(\frac{3}{48}\) = \(\frac{3}{4}\) Remaining work = 1 - \(\frac{3}{4}\) = \(\frac{1}{4}\) Now (16 men’s + 16 women’s) 2 days’ work = 2\(\big(\frac{1}{24}+\frac{1}{48}\big)\) = 2 x \(\frac{1}{16}\) = \(\frac{1}{8}\) \(\therefore\) Remaining work = \(\frac{1}{4}\) - \(\frac{1}{8}\) = \(\frac{1}{8}\) \(\frac{1}{384}\) work is done in 1 day by 1 man \(\therefore\) \(\frac{1}{8}\) work will be done in 2 days by \(\big(384\times\frac{1}{8}\times\frac{1}{2}\big)\) = 24 men.

Twenty four men can complete a work in sixteen days. Thirty two women can complete the same work in twenty four days. Sixteen men and sixteen women started working and worked for 12 days. How many more men are to be added to complete the remaining work in 2 days ? (a) 16 (b) 24 (c) 36 (d) 48

Answer»

(b) 24

1 man’s 1 days’ work = \(\frac{1}{24\times16}\)

\(\therefore\) 16 men’s 1days’ work = \(\frac{16}{24\times16}\) = \(\frac{1}{24}\)

1 woman’s 1 days’ work = \(\frac{1}{32\times24}\)

16 women’s 1 days’ work = \(\frac{16}{32\times24}\) = \(\frac{1}{48}\)

\(\therefore\) 12 days’ work of (16 men + 16 women) = 12\(\big(\frac{1}{24}+\frac{1}{48}\big)\)

= 12\(\big(\frac{2+1}{48}\big)\) = 12 x \(\frac{3}{48}\) = \(\frac{3}{4}\)

Remaining work = 1 - \(\frac{3}{4}\) = \(\frac{1}{4}\)

Now (16 men’s + 16 women’s) 2 days’ work = 2\(\big(\frac{1}{24}+\frac{1}{48}\big)\) = 2 x \(\frac{1}{16}\) = \(\frac{1}{8}\)

\(\therefore\) Remaining work = \(\frac{1}{4}\) - \(\frac{1}{8}\) = \(\frac{1}{8}\)

\(\frac{1}{384}\) work is done in 1 day by 1 man

\(\therefore\) \(\frac{1}{8}\) work will be done in 2 days by \(\big(384\times\frac{1}{8}\times\frac{1}{2}\big)\) = 24 men.