If 6 men and 10 women can do a piece of work in 15 days and 5 men and 9 women can do it in 17 days,

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21 Jun 2018 Work & Time

If 6 men and 10 women can do a piece of work in 15 days and 5 men and 9 women can do it in 17 days,

how many days will 5 men and 12 women take to do it?

OPtion

1) 13.75
2) 12.50
3) 13.33
4) 12.33
5) 13.60
6) 14.50
7) 14.33
8) 13.75
9) 14.66
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 = 15(6x + 10y) = 17(5x + 9y)

Solving we get, 90x - 85x = 153y - 150y
=> 5x = 3y
=> y = (5/3)x


Now, 6 x + 10 y can do work in 15 days.
So, 6x + (50/3) x can do work in 15 days.
So, 68x/3 can do work in 15 days.

Now, 5x + 12y = 5x + 20x = 25x

Hence, if 68x/3 can do work in 15 days, 25x can do work in (13*34)/39 = 13.6 days.

Option 5)

Correct Option: 5 Best Solution (9)

ARINJOY GHOSH   6 years AGO

let, A man can work 'm' per day
& A woman can work 'w' per day
Required day for complete the work for 5men and 12 women =d
(6m+10w)*15=1.......................................(i)
(5m+9w)*17=1.........................................(ii)
(5m+12w)*d=1........................................(iii)
(i)-(ii)
5m=3w
now, from (ii)
12*17w=1
w=1/204
now, from (iii)
15*1/204*d=1
d=204/15=13.60
Ans.(5)

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Varun   6 years AGO

Men = m, women = w
6m+10w = 1/15
5m+9w = 1/17
=> m = 1/340
w = 0.004590196

So, 5m+12w = 0.0735294 = 1/13.6
= > Answer is option (5)

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SAYAN CHATTERJEE   6 years AGO

6/M+10/F=1/15
5/M+9/F= 1/17.
On solving, M= 333.33 & F = 204.
So, 5 men and 12 women need 1/(5/333.33+12/204) = 13.54
Option 5.

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ruby   6 years AGO

Total Work is
15(6m+10w)+17(5m+9w)
5m=3w
--------------------------
6m+10w=1/15(1 day work)---> (1)
5m+9w=1/17----------------------> (2)
By solving (1) & (2) we get
1w = 1/204---------------->(3)
From question
5m+12w=?
3m+12w=15w
if 1w 204 days then 15 women?
204/15= 13.6days

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Deepshi Verma   6 years AGO

let 1 man 1day's work be x and 1 women's 1 day's work = y
Now we know that if 1 man a can do a piece a of work in n days, then in 1 day his work will be (1/n).
So applying this on the given question we will get
6x+10y = (1/15)
5x+9y = (1/17)

On solving these two we will get
x = (1/340) , y = (1/204)

hence 5 men , 12 women 1 day's work will be
5x+12y
Substitute the value of x and y and you will get
5/68

Now if 1day's work = 1/n, then work will be completed in n days.

So the answer is 68/5 i.e 13.60

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Sangeetha S   6 years AGO

Let 1 man's 1 day's work=x and 1 woman's 1 day's work=y
Solving , x= 3/1020 and y=5/1020
(5 men + 12 women)'s 1 day's work =((5*3/1020)+(12*5/1020))=75/1020=15/204
So finally finish the work in 204/15=13.60

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Titir Misra   6 years AGO

let work done by 1 man in 1 day =m and 1 women in 1 day=w
work done by 6 men and 10 women in 1 day = 1/15
work done by 5 men and 9 women in 1 day = 1/17
Solving we get m=1/340 and w=1/204
work done by 5 men and 12 women in 1 day =5*(1/340)+12*(1/204)=5/68
Time taken by 5 men and 12 women to do the work = 68/5 = 13.60

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abhishek bansal   6 years AGO

1 women do 1.25 unit work per day and men do .75 unit work per day

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G.S.Kantharao   6 years AGO

6m+10w=15d=>90m+150w=1d
5m+9w=17d=>85m+153w=1d
90m+150w=85m+153w
90m-85m=153w-150w
5m=3w
5m+9w=3w+9w=12w=17d
5m+12w=3w+12w=15w
=17*12/15=204/15=13.60d
My option is 5👈

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