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If 12 men and 16 women can do a piece of work in 5 days and 13 men and

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GeminiHeat
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If 12 men and 16 women can do a piece of work in 5 days and 13 men and [#permalink] New post   11 Apr 2022, 03:34
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If 12 men and 16 women can do a piece of work in 5 days and 13 men and 24 women can do it in 4 days, how long will 7 men and 10 women take to do it?

(A) 4.2 days
(B) 6.8 days
(C) 8.3 days
(D) 9.8 days
(E) 10.2 days
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C
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Nezamsohel
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Re: If 12 men and 16 women can do a piece of work in 5 days and 13 men and [#permalink] New post   11 Apr 2022, 09:35
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Solution with explanation
It’s a time work based General and-and related math
Efficiency of Man and Women
(12M+16W)*5=(13M+24W)*4
60M+80W=52M+96W
8m=16W
M:W=2:1
Now, (12*2+16*1)*5=(7*2+10*1)*D
200=24D
D=8.333 (Answered)
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Re: If 12 men and 16 women can do a piece of work in 5 days and 13 men and [#permalink] New post   28 Jun 2024, 06:02
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Alternatively

Let rate of one man be x and that of one woman be y


12x + 16y = 1/5...........1

13x + 24y = 1/4.............2


y = 1/200, x = 1/100

Let days required for 7 men and 10 women do job be d

0.12 = 1/d

d = 8.3333

Answer C

Adewale Fasipe, quant instructor from Lagos Nigeria.
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Jeeth15
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Re: If 12 men and 16 women can do a piece of work in 5 days and 13 men and [#permalink] New post   03 Jul 2024, 21:42
adewale223 wrote:
Alternatively

Let rate of one man be x and that of one woman be y


12x + 16y = 1/5...........1

13x + 24y = 1/4.............2


y = 1/200, x = 1/100

Let days required for 7 men and 10 women do job be d

0.12 = 1/d

d = 8.3333

Answer C

Adewale Fasipe, quant instructor from Lagos Nigeria.


In the 2 equations, I tool RHS as 5 and 4 instead of 1/5 and 1/4, and ended up getting y<0.
But I'm not sure why did I do that? adewale223, could you pls help.
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adewale223
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Re: If 12 men and 16 women can do a piece of work in 5 days and 13 men and [#permalink] New post   03 Jul 2024, 23:41
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Jeeth15 wrote:
adewale223 wrote:
Alternatively

Let rate of one man be x and that of one woman be y


12x + 16y = 1/5...........1

13x + 24y = 1/4.............2


y = 1/200, x = 1/100

Let days required for 7 men and 10 women do job be d

0.12 = 1/d

d = 8.3333

Answer C

Adewale Fasipe, quant instructor from Lagos Nigeria.


In the 2 equations, I tool RHS as 5 and 4 instead of 1/5 and 1/4, and ended up getting y<0.
But I'm not sure why did I do that? adewale223, could you pls help.




If you take take the sums as 5 and 4 in the two equations, they wont correspond because the sums represent rate, so what they equals to has to be rate as well.
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Re: If 12 men and 16 women can do a piece of work in 5 days and 13 men and [#permalink]
03 Jul 2024, 23:41
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