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Bunuel
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13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 wome 09 Jan 2021, 10:38
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71% (02:25) correct 29% (02:41) wrong based on 250 sessions

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13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy and 1 woman working together finish the same job (assume constant rates each for men, women, and boys)?

A. 21
B. 24
C. 42
D. 54
E. 63
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C
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13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 wome 09 Jan 2021, 10:50
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Bunuel
13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy and 1 woman working together finish the same job (assume constant rates each for men, women, and boys)?

A. 21
B. 24
C. 42
D. 54
E. 63
Show more


13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days.
So when we add all, that is (13 men and 7 boys ) + (6 boys and 13 women)=13 men+13 boys+13women, their one day work = \(\frac{1}{7}+\frac{1}{6}=13/42\).
So 13 of each can finish work in 42/13 days.
Thus 1 of each will take 13 times more = 13*42/13=42 days.

C
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TarunKumar1234
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13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 wome 09 Jan 2021, 13:21
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Given, 13 men and 7 boys can finish a job in 7 days, So, in 1 day work done by team = 1/7 work
Another case, 6 boys and 13 women can finish the same job in 6 days, So, in 1 day work done by team = 1/6 work

Now, adding resources for 1 day work.
So, 13 men, 13 women and 13 boys will complete in 1 day = 1/7 +1/6 = 13/42 work
or, 13 men, 13 women and 13 boys will complete 1 work in = 42/13 days
or, 1 man, 1 woman and 1 boy will complete 1 work in = 42/13 *13 = 42days

So, It is C. :)
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13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 wome 09 Jan 2021, 15:37
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13M + 7B = 1/7
13W + 6B = 1/6

sum the above equations

13W + 13M + 13B = 13/42

W + M + B = 1/42

Ans. C
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13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 wome 10 Jan 2021, 06:40
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chetan2u
Bunuel
13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy and 1 woman working together finish the same job (assume constant rates each for men, women, and boys)?

A. 21
B. 24
C. 42
D. 54
E. 63


13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days.
So when we add all, that is (13 men and 7 boys ) + (6 boys and 13 women)=13 men+13 boys+13women, their one day work = \(\frac{1}{7}+\frac{1}{6}=13/42\).
So 13 of each can finish work in 42/13 days.
Thus 1 of each will take 13 times more = 13*42/13=42 days.

C
Show more

hey chetan2u

i used another approach but got stuck ... can you help pls :)

\(\frac{(13m+7b)}{(6b+13w)} = \frac{6}{7}\)

so i get from above equation this 7m+b=6w

now normally i would use appropriate value from here 7m+b=6w and substitute into one of these 13m+7b or 6b+13w and compare it with m+b+w but i dont see such value for substitution

can you solve it using my approach ? if not why ? :)

happy happy new year :)
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13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 wome 10 Jan 2021, 08:56
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dave13
chetan2u
Bunuel
13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days. In how many days can 1 man, 1 boy and 1 woman working together finish the same job (assume constant rates each for men, women, and boys)?

A. 21
B. 24
C. 42
D. 54
E. 63


13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 women can finish the same job in 6 days.
So when we add all, that is (13 men and 7 boys ) + (6 boys and 13 women)=13 men+13 boys+13women, their one day work = \(\frac{1}{7}+\frac{1}{6}=13/42\).
So 13 of each can finish work in 42/13 days.
Thus 1 of each will take 13 times more = 13*42/13=42 days.

C

hey chetan2u

i used another approach but got stuck ... can you help pls :)

\(\frac{(13m+7b)}{(6b+13w)} = \frac{6}{7}\)

so i get from above equation this 7m+b=6w

now normally i would use appropriate value from here 7m+b=6w and substitute into one of these 13m+7b or 6b+13w and compare it with m+b+w but i dont see such value for substitution

can you solve it using my approach ? if not why ? :)

happy happy new year :)
Show more


Hi
dave13, Happy New year to you and your loved ones too!! :please: :)

Quote:
can you solve it using my approach ?
Show more

Yes, you can take your solution further.
Now 7m+b=6w => 13m+7b=6m+7m+b+6b=6m+6b+(7m+b)=6m+6b+6w=6(m+b+w)

Thus 13m+7b or 6(m+b+w) can do it in 7 days, m+b+w will take 6 times more time => 6*7=42
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13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 wome 24 Oct 2022, 21:39
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Using quation to solve, it can be started with
1) 13men+6boy = 1/7 complete 1/7 each working day
2) 7boy + 13 women = 1/6
1)+2) = 13 m+13w+13b=1/7+1/6=13/42
divided by 13 on each side
m+w+b= 1/42, which mean 42 days requried.
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13 men and 7 boys can finish a job in 7 days, while 6 boys and 13 wome 08 Apr 2025, 04:06
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