If 6 men and 8 women can do a piece of work in 10 days and 4 men and 7 women can do it in 12 days, h

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02 May 2018 Work & Time

If 6 men and 8 women can do a piece of work in 10 days and 4 men and 7 women can do it in 12 days, how many days will 4 men and 12 women take to do half of work?

OPtion

1) 3.66
2) 7.50
3) 3.33
4) 3.00
5) 6.5
6) 7.0
7) 3.25
8) 6.75
9) 8.00
10) None of these

Solution

Let a man's daily work is x units and that of a woman is y units.
So total amount of work, W = 10(6x + 8y) = 12(4x + 7y)

Solving we get, 60x - 48x = 84y - 80y
=> 12x = 4y
=> y = 3x


Now, 6 x + 8 y can do work in 10 days.
So, 6x + 24x can do work in 10 days.
So, 30 x can do work in 10 days.

Now, 4x + 12y = 4x + 36x = 40x

Hence, if 30 x can do work in 10 days, 40x can do work in (10*30)/40 = 7.5 days.

Half of work would be done in = 7.50/2 = 3.75

Option 10)

Correct Option: 10 Best Solution (6)

Dr.Dipin Singh   6 years AGO

6M+8W can complete work in 10 days.
4M+7W can complete work in 12 days
10*(6M+*W)= 12*(4M+7W)
1W=3M
6M+8W= 30M
4M+12W=40M
30 M complete full work in 10 days
40M will complete half work in (30*10)/(40*2)= 3.75 days

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DEBABRATA MARTHA   6 years AGO

6m+8w=12
4m+7w=10
by substraction w=6/5 and m=2/5
so 4m+12w=16
days required to complete half of the work=60/16=3.75

Like? Yes (2) | No (2)  

Prashant kumar   6 years AGO

(6M + 8 W)*10= (4M + 7W)*12
Total work ratio of M:W = 1:3
Toatl work =300 unit
half of work=150 untit
4 M + 12 Women = 150/10=3.75
Answer : None of these

Like? Yes (1) | No (2)  

SAYAN CHATTERJEE   6 years AGO

6/x+8/y = 1/10
4/x+ 7/y= 1/12
On solving, we get, x= 300 and y = 100
So, time reqd for finishing half the job = 0.5*1/(4/300+12/100) =
3.75.
Option 10.

Like? Yes | No (2)  

ruby   6 years AGO

Total work
10(6m+10w)=12(4m=8w)
by solving we get
1w=3m,
applying this in given eqn
6m+8*3m=1/10
30m=1/10
1m=300days
we need to find for 4m+12w
4m+12*3m=40m=300
m=300/40/2(half work)
m=3.75

Like? Yes | No (2)  

G.S.Kantharao   6 years AGO

6m+8w can do in =10d
60m+80w=1day
4m+7w can do in=12d
48m+84w=1d
60m+80w=48m+84w
12m=4w
1w=3m
6m+8w=6m+24m=10d
4m+12w=4m+36m=40m=1/2works in =(1/2)*10*(30/40)=15/4=3.75d
Hence the right option is 10👈

Like? Yes (1) | No (4)