Ten women can complete a piece in 15 days. Six men can complete the sa

1.	Ten women can complete a piece in 15 days. Six men can complete the same piece of work in 10 days. In how many days can 5 women and six men together complete the piece of work ? (a) 15 days (b) 7.5 days (c) 9 days (d) 12.5 days
Answer» (b) 7.5 days 10 women can complete a piece of work in 15 days \(\therefore\) 1 woman can complete in 1 day, \(\frac{1}{10\times15}\) = \(\frac{1}{150}\) part of work 6 men can complete the same work in 10 days, \(\therefore\) 1 man can complete in 1 day, \(\frac{1}{6\times10}\) = \(\frac{1}{60}\) part of the work \(\therefore\) (6 men’s + 5 women’s) 1 days’ work = \(\frac{6}{60}\)+ \(\frac{5}{150}\) = \(\frac{1}{10}\) + \(\frac{1}{30}\) = \(\frac{3+1}{30}\) = \(\frac{4}{30}\) = \(\frac{2}{15}\) \(\therefore\) 6 men and 5 women can complete the whole work in \(\frac{15}{2}\) = 7.5 days

Ten women can complete a piece in 15 days. Six men can complete the same piece of work in 10 days. In how many days can 5 women and six men together complete the piece of work ? (a) 15 days (b) 7.5 days (c) 9 days (d) 12.5 days

Answer»

(b) 7.5 days

10 women can complete a piece of work in 15 days

\(\therefore\) 1 woman can complete in 1 day, \(\frac{1}{10\times15}\) = \(\frac{1}{150}\) part of work

6 men can complete the same work in 10 days,

\(\therefore\) 1 man can complete in 1 day, \(\frac{1}{6\times10}\) = \(\frac{1}{60}\) part of the work

\(\therefore\) (6 men’s + 5 women’s) 1 days’ work

= \(\frac{6}{60}\)+ \(\frac{5}{150}\) = \(\frac{1}{10}\) + \(\frac{1}{30}\) = \(\frac{3+1}{30}\) = \(\frac{4}{30}\) = \(\frac{2}{15}\)

\(\therefore\) 6 men and 5 women can complete the whole work in \(\frac{15}{2}\) = 7.5 days