4 men can complete a piece of work in 2 days. 4 women can complete the same piece of work in 4 days whereas 5 children can complete the same piece of work in 4 days. If, 2 men, 4 women and 10 children work together, in how many days can the work be completed?
(a) 1 day
(b) 3 days
(c) 2 days
(d) 4 days
(e) None of these
Solution: (a)
4 × 2 men = 4 × 4 women = 5×4 children
\(\displaystyle \Rightarrow \) 2 men = 4 women = 5 children
1 man can do the work in 8 days. 1 woman can do the work in 16 days. 1 child can do the work in 20 days. 2m + 4w + 10c can do the work in – \(\displaystyle \left( {\frac{2}{8}+\frac{4}{{16}}+\frac{{10}}{{20}}} \right)\times \)d = 1 \(\displaystyle \Rightarrow \left( {\frac{1}{4}+\frac{1}{4}+\frac{1}{2}} \right)\times \)d = 1 \(\displaystyle \Rightarrow \)d = 1
Six women and 10 children together take six days to complete a piece of work. How many days will 10 children take to complete the piece of work if six women together can complete the same piece of work in 10 days?
(a) 21
(b) 18
(c) 12
(d) 15
(e) None of these
Solution: (d)
Work done by 6 women in 1 day = \(\displaystyle \frac{1}{{10}}\)
Work done by 6 women in 6 days = \(\displaystyle \frac{6}{{10}}=\frac{3}{5}\)
Therefore, Remaining work = \(\displaystyle (1-\frac{3}{5})=\frac{2}{5}\) which is completed by 10 children in 6 days
Therefore, Work done by 10 children in 1 day = \(\displaystyle \frac{2}{{5\times 6}}=\frac{1}{{15}}\)
Therfore, Time taken in completing the work = 15 days.
Alternate Method:
Number of days required = \(\displaystyle \frac{{6\times 10}}{{10-6}}=\frac{{6\times 10}}{4}=15days\)
2 women and 10 children together take 8 days to complete a piece of work. How many days will 10 children alone take to complete the piece of work if 8 women alone can complete the piece of work in 6 days ?
(a) 15
(b) 12
(c) 10
(d) 24
(e) None of these
Solution: (b)
8 women can do a work in 6 days.
Therefore, 2 women can do same work in = \(\displaystyle \frac{{8\times 6}}{2}=24days\)
2 women can do \(\displaystyle \frac{1}{{24}}\) work in 1 day.
(2 women + 10 children) can do a work in 8 days.
Therefore, (2 women + 10 children)’s 1 days work \(\displaystyle \frac{1}{8}\).
10 Children 1 day work = \(\displaystyle \frac{1}{8}-\frac{1}{{24}}=\frac{1}{{12}}\) work
Hence 10 children can do same work in 12 days.
Alternate method
Consider the speed of work of women as ‘X’ and that of children be ‘Y’ and the Work as ‘W’, then
2X+10Y=W/8 and
8X=W/6
\(\displaystyle \Rightarrow \) X=W/48
Y substituting the value of X in first equation, we get
2(W/48)+10Y=W/8
Y=W/120
\(\displaystyle \Rightarrow \) Speed of 1 Child = W/120
\(\displaystyle \Rightarrow \) Speed of 10 Child = W/12
Hence 10 children can do same work in 12 days.
A and B together can complete a particular task in 8 days. If B alone can complete the same task in 10 days, how many days will A take to complete the task if he works alone ?
Then in 1 day (A+B) will do 80/10 = 10 unit of work
Therefore, A does 2 unit of work each day
Hence, A requires 80/2 = 40 days to complete work
Two pipes can full a tank in 10 h and 16 h respectively. A third pipe can empty the tank in 32 h. If all the three pipes function simultaneously, then in how much time the tank will be full? (in hours)
A alone can make 100 baskets in 6 days and B alone can make 100 baskets in 12 days. In how many days can A and B together make 100 baskets?
(a) 3 days
(b) 5 days
(c) \(\displaystyle 2\frac{1}{2}days\)
(d) \(\displaystyle 3\frac{1}{2}days\)
(e) None of these
Solution: (e)
A’s 1 day’s work = \(\displaystyle \frac{1}{6}\)\(\displaystyle \frac{1}{6}\)
B’s 1 day’s work = \(\displaystyle \frac{1}{{12}}\)
Therefore, (A + B)’s 1 day’s work = \(\displaystyle \frac{1}{6}+\frac{1}{{12}}=\frac{{2+1}}{{12}}=\frac{1}{4}\)
Hence, A and B together will make 100 baskets in 4 days.
Alternate method
A alone can make 100 baskets in 6 days and B alone can make in 12 days.
Therefore, Rate of efficiency of A=100/6 baskets per day
And rate of efficiency of B=100/12 baskets per day
⇒ Baskets made by A and B together in 1 day = \(\displaystyle \frac{{100}}{6}+\frac{{100}}{{12}}=\frac{{300}}{{12}}=25\) baskets per day
Therefore, Time taken by A and B together to make 100 baskets= \(\displaystyle \frac{{100}}{{25}}\)=4 days
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