10 men & 15 women complete half of the work in 12 days and 6 men & 15 women complete one third of th

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06 Oct 2011 work

10 men & 15 women complete half of the work in 12 days and 6 men & 15 women complete one third of the work in 10 days. How many days are required to complete the same full work by taking 10 men and 30 women?

OPtion

1) 12
2) 16
3) 18
4) 20
5) 21
6) 24
7) 27
8) 30
9) data are insufficient
10) none of these

Solution

10 men & 15 women complete half of the work in 12 days
so 20 men and 30 women complete the work in 12 days
so 240 men and 360 women complete the work in 1 day
similarly 6 men & 15 women complete one third of the work in 10 days
so 18 men and 45 women complete the work in 10 days
so 180 men and 450 women complete the work in 1 day
on comparing 240 men 360 women = 180 men 450 women
or 60 men = 90 women
so 2 men = 3 women
now 10 men 15 women = 20 men
and 10 men 30 women = 30 men
it is given that 20 men complete the work in 24 days
so 30 men will do the same work in 24*20/30 = 16 days

Correct Option: 2 Best Solution (9)

HARMEET KAUR   12 years AGO

10 men & 15 women complete half of the work in 12 days and 6 men & 15 women complete one third of the work in 10 days.
hence
1 man = 1.5 women

10 men and 30 women or 45 women will complete the work in 16 days.

Like? Yes (5) | No (1)  

CHANDAN KR SINGH   12 years AGO

ANSWER : 2. 16 days

SOLUTION :

Assume 1 man in 1 day do x work and 1 women in 1 day do y work.
So
10x + 15y = 1/24
6x + 15y = 1/30
solving we get
x = 1/480
y = 1/720
so 10 men & 30 women in 1 day do 10/48 + 30/720 = 1/16 of work.
Whole work in 16 days.

Like? Yes (4) | No   

Dr.Dipin Singh   12 years AGO

10 men & 15 women complete half of the work in 12 days .
10 men & 15 women complete full work in 24 days .
240 men & 360 women complete full work in 1 day.
6 men & 15 women complete one third of the work in 10 days.
6 men & 15 women complete one third full work in 30 days.
180 men & 450 women complete one full work in 1 day.

240 men & 360 women = 180 men & 450 women
60 men = 90 women
1 men = 1.5 women
180 men = 270 women
180 men & 450 women complete one full work in 1 day.
720 women complete one full work in 1 day.
10 men and 30 women = 45 women

45 women complete one full work in 720/45 = 16 days

Like? Yes (4) | No (2)  

Gunaseelan   12 years AGO

Let x be one man's one day work.
Let y be one women's one day work.

Given 10x+15y=1/24
6x+15y=1/30

By Solving this eqn, we get x=1/480
y=1/720

10(1/480)+30(1/720)=1/48+1/24=1/16
So 10 men and 30 women can complete their work in 16 days.

Like? Yes (4) | No (2)  

Mullaji Zubair Dawood   12 years AGO

Let Men\'s Effort=\'x\' & Women\'s=\'y\' then
Given data is
{12days(10x+15y)=1/2 work} &
{10days(6x+15y)=1/3 work}
By solving eqns Simulteneously,we Get 10x=15y=3/144,
.\'.x=3/1440&y=1/720,BUT to Complete Full Work
{\'z\'days[(10*3)/1440]+[(30*1)/720]=1)}
We GET z=16days which is 2nd Answer..

Like? Yes (2) | No   

UMESH SINGLA   12 years AGO

10 men and 15 women do half work in 12 days,
hence it will take them 24 days for completng the whole work.
=> 10x+15y=1/24
similarly
6x+15y=1/30
on solving above two.
1 men alone can do complete work in 480 days
1 Women alone can do complete work in 720 days.
10 men and 30 women 10*1/480+30*1/720=1/16
hence 10 men and 30 women can finish work in 16 days

Like? Yes (2) | No (1)  

sridhar reddy   12 years AGO

Let capacity of men x and women y in one day
10x+15y can complete half of the work in 12 days
in one day 1/24 work can be completed
ie.,10x+15y=1/24
and
6x+15y can complete one third of the work in 10 days
in one day they can complete 1/30 work
ie.,6x+15y = 1/30
by solving these two linear equations
we will get
the capacity of man x = 1/480 and woman y = 1/240
=10x+30y
=10*1/480 + 30*1/240
=1/16 in one day
10 men and 30 women can complete the work in 16 days

Like? Yes (2) | No (1)  

Abhay Singh   12 years AGO

10 men and 15 women 1 day work = 1/24
6 men and 15 women 1 day work = 1/30 then
4 men 1 day work = 1/120 i.e
4 men complete work in 120 days,then 10 men= 48 days
similarly, 15w one day work=1/48
i.e 15w complete work in 48 days,then
30w complete in 24days
then 10men and 30 women 1 day work =
1/48 + 1/24= 1/16
hence work completed in 16 days.

Like? Yes (1) | No   

arjun   12 years AGO

let 1 mans 1 days work=x;
1 woman 1 days work=y;
according to question 10men and 15 women can complete a work in 24 days
and 6 man and 15 women can complete same work in 30 days .
so 10x+15y=1/24;
and 6x+15y=1/30;
now solving both equations we get:
x=1/480 and y=1/720;
so query for 10 man and 30 woman :
1/days=10/480+30/720=1/16
hence days are 16.
option no 2. 16(ans)

Like? Yes (2) | No (1)