Latest CAT Aptitude Question SOLUTION: 4 men & 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

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(#M40038196) CAT Category question ss Keep an EYE

4 men & 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

Asked In CAT MohanRaj (9 years ago)

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vamshi  (9 years ago)

let 1 Man alone completes work in M days, then man's 1 day work is 1/M
let 1 woman alone completes work in M days, then woman's 1 day work is 1/W

given
4 M & 6 W complete work in 8 days,then 4 M & 6 W , 1 day work is 1/8
3 M & 7 W complete work in 10 days,then 3 M & 7 W , 1 day work is 1/10

so we get 1 day work equations as
4(1/M)+6(1/w)=1/8
3(1/m)+7(1/w)=1/10

on eliminating 1/M
i/w = 1/40
=>w = 40

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Ravi Kumar  (9 years ago)

sorry ans is 40
Let a man can complete m work in a day
and a woman can complete w work in a day
=> (4m + 6w) * 8 = 1 and (3m + 7w) * 10 = 1
=> 4m + 6w = 1/8 ... (1)
and 3m + 7w = 1/10 ... (2)
Solving eqns. (1) and (2),
m = (1/10) (7/8 - 6/10) = 11/400 and
w = (1/10) (4/10 - 3/8) = 1/400

=> one woman can do 1/400 of work in a day
and 10 women can do 1/40 of the work
=> to complete the work,
10 women will take 40 days.

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rakesh yadav  (9 years ago)

Ans:40 days.

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Ravi Kumar  (9 years ago)

ans: 16 days.
solving two equation
4m+6w=8d
3m+7w=10d

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Abhishek Mitra  (9 years ago)

lets consider,total work is 1
one man can do x in 1 day
and one woman can do y in 1 day
so the two equations will be
1)4x+6y=1/8
2)3x+7y=1/10
solving this two we get 10y=1/40
i.e. 10y is work done by 10 women in 1 day
so they will take (1/10y) days to complete the job
i.e. 40 days
so the ANSWER is 40 days

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