20 women work for 4 days on a certain project and complete one-tenth of it. 15 men work for the next

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29 Sep 2022 Time & Work

20 women work for 4 days on a certain project and complete one-tenth of it. 15 men work for the next 'X' days and complete one-fifth of it, If after (4+X) days, 20 women and 15 men work together and complete the remaining work in 12 days, then how many days will 15 men take to complete the whole work ?

OPtion

1) 24
2) 30
3) 45
4) 60
5) 36
6) 48
7) 18
8) 27
9) 42
10) None of these

Solution

20 Women's 1 day work=1/(4*10)=1/40
15 men's 1 days work=1/(X*5)=1/(5X)
After total (4+X) days, work comleted=1/10 + 1/5=3/10 and remaining work=7/10
As 20 women and 15 men complete the remaining work in 12 days, so their 1 day work=(1/12)*(7/10)=7/120
Comparing 1 day's work of 20 women and 15 men=1/40 + 1/(5X)=7/120
(X+8)/(40X)=7/120
Solving, we get X=6
.'. 1 day's work of 15 men=1/(5*6)=1/30
Hence, 15 men can complete the whole work in 30 days.
Correct Option 2)

Correct Option: 2 Best Solution (1)

G.S.Kantharao   2 years AGO

20w - 4d -1/10 =>in 1d=1/40
15m- Xd - 1/5 => in 1d=1/5x
Remaining work =1-(1/10+1/5)=1 -3/10= 7/10
20w+15w - 12d - 7/10
12(1/40+1/5x)=7/10
12(x+8)/40x =7/10
12x+96=28x=>16x=96=>x=6
So 15m - 6d -1/5=>1d=1/30
Full work can be completed in =30d
My option is 2👈

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