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If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 [#permalink]
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09 Aug 2017, 01:12
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Re: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 [#permalink]
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09 Aug 2017, 01:23
Bunuel wrote: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys would it take to do a job four times as big working for 5 hours a day for 12 days?
A. 44 B. 50 C. 120 D. 122 E. 128 Hi... Let's count in terms of men.. 1 w = 20/24 m.....b = 1/2 m.. So if 20 m can do a work in 12*8 H, 20*12*8 m will do it in 1 h.. 4 times the work will require 12*8*4*20 m.. Working 5*12 per man , \(\frac{20*12*8*4}{5*12}=128m\) But 6w and 2b are also there.. 6w=6*20/24=5m....2b=2*1/2=1m.. So remaining men required=12851=122 D
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Re: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 [#permalink]
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09 Aug 2017, 01:41
Bunuel wrote: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys would it take to do a job four times as big working for 5 hours a day for 12 days?
A. 44 B. 50 C. 120 D. 122 E. 128 \(R_m = \frac{1}{12* 8 * 20}\) \(R_w = \frac{1}{12* 8 * 24}\) \(R_b = \frac{1}{12* 8 * 40}\) Let no. of men needed = x \((\frac{x}{12* 8 * 20} + \frac{6}{12*8*24}+\frac{2}{12*8*40} ) * 5*12 = 4\) \(\frac{6+x}{32} = 4\) \(x+6 = 128\) \(x = 122\) (choice D)



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If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 [#permalink]
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Updated on: 26 Aug 2017, 08:56
Bunuel wrote: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys would it take to do a job four times as big working for 5 hours a day for 12 days?
A. 44 B. 50 C. 120 D. 122 E. 128 20 men work for 12 days for 8 hours to do a job so number of men required to complete the work in 12 days working 5 hours = (20*8)/5 =32 as the work is 4 times as big as the previous one, so no of men required will be = 4*32 = 128 Now we already have 6 women and 2 boys. we need to convert them to men to find the remaining no of men required 24W=20M, or 6W=(20*6)/24 = 5 Men 40B=20M, or 2B = (20*2)/40 = 1 Men So number of men required = 128(5+1) = 122 Option D
Originally posted by niks18 on 09 Aug 2017, 02:05.
Last edited by niks18 on 26 Aug 2017, 08:56, edited 1 time in total.



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Re: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 [#permalink]
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09 Aug 2017, 21:12
niks18 wrote: Bunuel wrote: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys would it take to do a job four times as big working for 5 hours a day for 12 days?
A. 44 B. 50 C. 120 D. 122 E. 128 20 men work for 12 days for 8 hours to do a job so number of men required to complete the work in 12 days working 5 hours = (20*8)/5 =32 as the work is 4 times as big as the previous one, so no of men required will be = 4*32 = 128 No we already have 6 women and 2 boys. we need to convert them to men to find the remaining no of men required 24W=20M, or 6W=(20*6)/24 = 5 Men 40B=20M, or 2B = (20*2)/40 = 1 Men So number of men required = 128(5+1) = 122 Option DThis solution is short and clear.. I am trying to figure out how (20*8)/5 =32.. Is there a formula for this?



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If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 [#permalink]
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09 Aug 2017, 21:19
pclawong wrote: niks18 wrote: Bunuel wrote: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys would it take to do a job four times as big working for 5 hours a day for 12 days?
A. 44 B. 50 C. 120 D. 122 E. 128 20 men work for 12 days for 8 hours to do a job so number of men required to complete the work in 12 days working 5 hours = (20*8)/5 =32 as the work is 4 times as big as the previous one, so no of men required will be = 4*32 = 128 No we already have 6 women and 2 boys. we need to convert them to men to find the remaining no of men required 24W=20M, or 6W=(20*6)/24 = 5 Men 40B=20M, or 2B = (20*2)/40 = 1 Men So number of men required = 128(5+1) = 122 Option DThis solution is short and clear.. I am trying to figure out how (20*8)/5 =32.. Is there a formula for this? Hi pclawongas 12 days are constant for both the scenarios, let's not think about it. 20 men take 8 hours to complete the job No of men required if work is done only for 1 hour a day = 8*20 men(more men as hours worked are less) No of men required if work is done for 5 hours a day = (8*20)/5 (less men required now)



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Re: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 [#permalink]
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10 Aug 2017, 06:08
pclawong wrote: niks18 wrote: Bunuel wrote: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys would it take to do a job four times as big working for 5 hours a day for 12 days?
A. 44 B. 50 C. 120 D. 122 E. 128 20 men work for 12 days for 8 hours to do a job so number of men required to complete the work in 12 days working 5 hours = (20*8)/5 =32 as the work is 4 times as big as the previous one, so no of men required will be = 4*32 = 128 No we already have 6 women and 2 boys. we need to convert them to men to find the remaining no of men required 24W=20M, or 6W=(20*6)/24 = 5 Men 40B=20M, or 2B = (20*2)/40 = 1 Men So number of men required = 128(5+1) = 122 Option DThis solution is short and clear.. I am trying to figure out how (20*8)/5 =32.. Is there a formula for this? The solution above stems from the basics Work = number of labor * Rate * Time Because it is same work W1 = W2 n1 * R1 * T1 = n2 * R2 * T2 ( in this case, R1 = R2, so cancel out as each man have same rate) n1 * T1 = n2 * T2 From men's work numbers, apply in equation above 20 * 8 * 12 = n2 * 5 * 12 n2 = 20 * 8 / 5 ...............same result as described in previous post. I hope it helps



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Re: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 [#permalink]
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10 Aug 2017, 10:26
Bunuel wrote: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys would it take to do a job four times as big working for 5 hours a day for 12 days?
A. 44 B. 50 C. 120 D. 122 E. 128 Total Number of men needed = 20 * 4 * (8/5) = 128 (using the method discussed here: https://www.veritasprep.com/blog/2015/1 ... madeeasy/) Let's see how many we already have. Convert all workforce to men. 24 women = 20 men 6 women = 5 men 40 boys = 20 men 2 boys = 1 man So we already have 5 + 1 = 6 men. We need another 128  6 = 122 men.
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Re: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 [#permalink]
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15 Aug 2017, 10:51
Bunuel wrote: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys would it take to do a job four times as big working for 5 hours a day for 12 days?
A. 44 B. 50 C. 120 D. 122 E. 128 We can let the job = 1, and we are given that the job can be completed in 12 x 8 = 96 hours by 20 men or 24 women or 40 boys. Let’s determine the rate of 1 man per hour, which is (1/20)/96 = 1/(20 x 96). Similarly, the rate of 1 woman per hour is (1/24)/96 = 1/(24 x 96) and the rate of 1 boy per hour is (1/40)/96 = 1/(40 x 96). Now we are given that another job is four times as big, and thus this new job = 4. We also are given that 6 women, 2 boys, and some number of men will be working on this job for 5 x 12 = 60 hours. We need to determine the number of men needed. We can let the number of men needed = n and create the following equation: 6 * 1/(24 x 96) * 60 + 2 * 1/(40 x 96) * 60 + n * 1/(20 x 96) * 60 = 4 360/(24 x 96) + 120/(40 x 96) + 60n/(20 x 96) = 4 Multiplying the entire equation by 96, we have: 360/24 + 120/40 + 60n/20 = 384 15 + 3 + 3n = 384 3n = 366 n = 122 Answer: D
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Re: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 [#permalink]
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19 Sep 2017, 00:33
Bunuel wrote: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys would it take to do a job four times as big working for 5 hours a day for 12 days?
A. 44 B. 50 C. 120 D. 122 E. 128 We know the daily rate of: A) Man is 1/(20*12*8) = 1/1920 B) Woman is 1/2304 C) Boy is 1/3840 So, 1 man equals to 2 boys and 6 women produce as much as 5 men. So, we want to know how many men should we add to the 6 men (6 women plus 2 boys). Now, we know that 20 men need to work 1920 hours to complete one job, working 8h/day for 12 days. Since the second job is 4 times as big as the first one, it will need 1920*4 = 7680 hours from men. So, we should divide that amount of hours per 60 hours (the amount of hours each person can work in the second job, as in, 5h/day x 12 days). We'll have: 7680/60 = 128 men. So, we need 128 men in total. But since we already have 6 women and 2 boys already working (or 6 men), there will be 128122 men working alongside them.



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Re: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 [#permalink]
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03 Feb 2018, 06:27
Bunuel wrote: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys would it take to do a job four times as big working for 5 hours a day for 12 days?
A. 44 B. 50 C. 120 D. 122 E. 128 Since 20 men/24 women/40 boys can complete the piece of work, working 8 hours a day for 12 days we can assume the total work to be 20 * 8 * 12 units. 20 men:24 women:40 boys will translate to 1 man:1.2 woman:2 boys We need to the find the total number of men working to complete a work 4 times as large working for 12 days at 5 hours/day. If the number of men needed to complete 4*(20*8*12) units of work at 5*12 is x, we can calculate x as \(\frac{4*(20*8*12)}{5*12} = 128\) Now, we are told that 6 women and 2 boys will be helping the man complete the work. They would effectively do \(\frac{6}{1.2} + \frac{2}{2}\) or 5 + 1 = 6 men's work respectively. Therefore, the total men needed to complete the work along with 5 women and 2 boys is 128  6 = 122(Option D)
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Re: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 [#permalink]
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03 Feb 2018, 09:41
Bunuel wrote: If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 hours a day, how many men working with 6 women and 2 boys would it take to do a job four times as big working for 5 hours a day for 12 days?
A. 44 B. 50 C. 120 D. 122 E. 128 Let a be the number of men. Given, \(8*12*20m = 8*12*24w = 8*12*40b\) \(5m = 6w = 10b\) \((6w + 2b + a.m) = 4*8*12*24w\) \(6 + a = 128\) \(a = 122\)
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If 20 men or 24 women or 40 boys can do a job in 12 days working for 8 [#permalink]
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03 Feb 2018, 21:18
20 m = 24 w = 40 b > 6 w = 5 m and 2 b = 1 m > 6w + 2b = 6 m
by the Unitary method: (men*days*hours*efficiency) / work = K
= [(20*12*8)/ 1] = [((6+x)*5*12) / 4]
= x is 122.
Answer is D




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