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DisciplinedPrep
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8 men and 16 women can do a work in 8 days. 40 men and 48 women can do 14 Mar 2019, 23:02
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C
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55% (hard)

Question Stats:

73% (02:51) correct 27% (02:52) wrong based on 468 sessions

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8 men and 16 women can do a work in 8 days. 40 men and 48 women can do the same work in 2 days. How many days are required for 6 men and 12 women to do the same work?

A. \(15\) days
B. \(12\) days
C. \(10\frac{2}{3}\) days
D. \(10\) days
E. \(10\frac{1}{2}\) days
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C
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KarishmaB
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8 men and 16 women can do a work in 8 days. 40 men and 48 women can do 14 Mar 2019, 23:08
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DisciplinedPrep
8 men and 16 women can do a work in 8 days. 40 men and 48 women can do the same work in 2 days. How many days are required for 6 men and 12 women to do the same work?

A. \(15\) days
B. \(12\) days
C. \(10\frac{2}{3}\) days
D. \(10\) days
E. \(10\frac{1}{2}\) days
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Let M be the rate of work of men and W be the rate of work of women.

8M + 16W = 1/8 (since they complete 1/8th of the work every day)
M + 2W = 1/64

6M + 12W = ?
6*(1/64) = 3/32 of the work every day

So 6 men and 12 women will take 32/3 = 10(2/3) days to complete the work.

Answer (C)
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8 men and 16 women can do a work in 8 days. 40 men and 48 women can do 15 Mar 2019, 02:44
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Thanks mam.

I normally solve same work ps with following formula.
(Man 1) x (DAY 1)= (Man 2) x (DAY 2)

Here,
Man 1= 8M+16W=8(M+2W)
Day 1= 8
Man 2=6M+12W=6 (M+2W)
Day 2=??? (Assume P)


Now utilise the formula.
(Man 1) x (DAY 1)= (Man 2) x (DAY 2)

So, [8(M+2W) x 8] =[6 (M+2W) * P]

Or P=32/3. (Required time DAY2].

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8 men and 16 women can do a work in 8 days. 40 men and 48 women can do 23 Aug 2020, 15:17
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How I solved it:

8 men and 16 women do the work in 8 days:
64m+128w=1

40 men and 48 women do the same amount of work in 2 days:
80m+96w =1

solve the 2 equations

a man's rate is 1/128
a woman's rate is 1/256

(note: question appear's to be sexist, because the man works at a faster rate. JK. lolol)

the question how long does it take for 6 men and 12 women to complete the same amount of work, so:
x*( 6/128 + 12/256)=1

10 and (2/3) days
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8 men and 16 women can do a work in 8 days. 40 men and 48 women can do 24 Sep 2020, 06:40
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It takes only 30 sec to solve the math from 1st equation

8m+16w=8 days
8(1m+2w)=8 days
(1m+2w)=8*8 days
6(1m+2w)=8*8/6 days
6m+12w = 32/3 days

Ans : C
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8 men and 16 women can do a work in 8 days. 40 men and 48 women can do 16 Oct 2020, 15:05
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If 8 men and 16 women can do a job in 8 days, then they do 1/8th of the job each day.

8m + 16w = 1/8
(m + 2w) = 1/64
6(m+2w) = 6/64
6m + 12w = 3/32

rate = 3/32
time = 32/3 = 10 2/3 days

Answer is C.
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8 men and 16 women can do a work in 8 days. 40 men and 48 women can do Updated on: 25 Mar 2025, 09:47
Originally posted by imeanup on 29 Jan 2021, 21:49.
Last edited by imeanup on 25 Mar 2025, 09:47, edited 2 times in total.
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Method: Efficiency

The "Total Work" remains the same in both cases, we could find the efficiency of men and women as follows:

\((8m+16w) \times 8=(40m+48w) \times 2\), whereas m = men and w = women

\(32m+64w=40m+48w \Longrightarrow (1)\)

\(8m=16w\)

\(\dfrac{m}{w} = \dfrac{2}{1} \)

Thus, the efficiency of \(m=2\) and \(w=1\).

Next, we will find the "Total Work" and substitute the value of \(m,w\) in any one of the equation (1) above;

\(TW=(8\times 2+16 \times 1) \times 8 \ or \ (40\times 2+48 \times 1) \times 2 \)

\(TW=(8\times 2+16\times 1)\times 8 = 32\times 8\)


How many days are required for 6 men and 12 women to do the same work?

The \(TW\) is completed by a new set of men and women i.e. \((6m+12w)\) in (let's say) \(x\) days;

\(x=\frac{32\times 8}{(6\times 2+12\times 1)} = \frac{32}{3}=10\frac{2}{3}\)
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8 men and 16 women can do a work in 8 days. 40 men and 48 women can do 21 Mar 2026, 05:43
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