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18 Jul 2018, 01:32
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Difficulty:

95% (hard)

Question Stats:

42% (02:59) correct 58% (04:08) wrong based on 33 sessions

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If 5 men with 7 boys can earn 3825$in 6 days and 2 men with 3 boys can earn 1050$ in 4 days, in what time will 7 men with 6 boys earn 22500$? 1) 30 Days 2) 25 Days 3) 40 Days 4) 35 Days 5) 45 Days Math Expert Joined: 02 Aug 2009 Posts: 6521 Re: If 5 men with 7 boys can earn 3825$ in 6 days and 2 men with 3 boys ca  [#permalink]

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18 Jul 2018, 02:17
GoonerForever wrote:
If 5 men with 7 boys can earn 3825$in 6 days and 2 men with 3 boys can earn 1050$ in 4 days, in what time will 7 men with 6 boys earn 22500$? 1) 30 Days 2) 25 Days 3) 40 Days 4) 35 Days 5) 45 Days Let men earn m per day and boys earn b per day... So 3825 in 6 days means 3825/6=1275/2 per day Thus 5m+7b=1275/2......(I) 1050 in 4 days means 1050/4=525/2 per day Thus 2m+3b=525/2.....(II) Multiply I by 2...... 10m+14b=1275 And II by 5............ 10m+15b=2625/2 Subtract them 10m+15b-(10m+14b)=2625/2-1275=75/2..........so b=75/2 Add I and II.. 5m+7b+2m+3b=1275/2+525/2........7m+10b=1800/2=900 But we are looking for 7m+6b... b=75/2, so 4b=4*75/2=150 Thus 7m+10b-4b=900-150.......7m+6b=750 So one day earnings of 7 men and 6 boys is 750, 22500 Will be in 22500/750=30 days A _________________ 1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372 2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html 3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html GMAT online Tutor e-GMAT Representative Joined: 04 Jan 2015 Posts: 1888 Re: If 5 men with 7 boys can earn 3825$ in 6 days and 2 men with 3 boys ca  [#permalink]

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18 Jul 2018, 02:59

Solution

Given:

• 5 men with 7 boys can earn 3825$in 6 days • 2 men with 3 boys can earn 1050$ in 4 days

To find:

• In how many days will 7 men with 6 boys earn 22500$Approach and Working: Let us denote men by ‘M’ and boys by ‘B’. • In 6 days, 5 men with 7 boys earns 3825$.
o Hence, 6(5M+7B)=3825
o 30M+42B= 3825--------------(1)

• In 4 days, 2 men with 3 boys earns 1050$. o Hence, 4(2M+3B)= 1050 o 8M+12B= 1050 o $$M=\frac{(1050-12B)}{8}$$ o $$M= \frac{1050}{8}-\frac{3B}{2}$$  Substituting the value of M in equation 1, we get:  $$\frac{30*1050}{8}- \frac{30*3B}{2}+42B= 3825$$  $$\frac{15*525}{2}-45B+42B= 3825$$  3B= 112.5 • B= 37.5 • M=75 • Hence, 7M+6B=750 • Hence, 7 men with 6 boys will earn 22500$ in$$\frac{22500}{750}=30$$days.

Hence, the correct answer is option A.

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Re: If 5 men with 7 boys can earn 3825$in 6 days and 2 men with 3 boys ca [#permalink] ### Show Tags 22 Jul 2018, 18:34 GoonerForever wrote: If 5 men with 7 boys can earn 3825$ in 6 days and 2 men with 3 boys can earn 1050$in 4 days, in what time will 7 men with 6 boys earn 22500$ ?

1) 30 Days
2) 25 Days
3) 40 Days
4) 35 Days
5) 45 Days

We can let m = the amount of money a man earns per day and b = the amount of money a boy earns per day.

If 5 men with 7 boys can earn $3825 in 6 days, then they earn 3825/6 =$637.50 a day. So 5m + 7b = 637.5. Similarly, if 2 men with 3 boys can earn $1050 in 4 days, then they earn 1050/4 =$262.50 a day. So 2m + 3b = 262.5.

Let’s multiply the first equation by 2, obtaining 10m + 14b = 1275.

Let’s multiply the second equation by 5, obtaining 10m + 15b = 1312.5.

Subtracting the second new equation from the first new equation, we have:

-b = -37.5

b = 37.5

Substitute this in the second equation:

2m + 3(37.5) = 262.5

2m + 112.5 = 262.5

2m = 150

m = 75

Therefore, 7 men with 6 boys earn 7(75) + 6(37.5) = $750 a day, and it will take them 22,500/750 = 30 days to earn$22,500.

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Re: If 5 men with 7 boys can earn 3825$in 6 days and 2 men with 3 boys ca [#permalink] ### Show Tags 23 Jul 2018, 05:25 5 M 7 B - 6 days - 3825$
---> 10 M 14 B - 6 days - 7650$- Eq1 also, 2 M 3 B - 4 days - 1050$
---> 10 M 15 B - 4 days - 5250$---> 10 M 15 B - 6 days - 7875$ -Eq2

From Eq1 and Eq2
1 B - 6 days - 225$- Eq 3 From eq 1 and Eq 3 10M - 6days - 4500$
or 1 M - 6days - 450$that is 1M = 2 B so 7M and 6B = 10 M = 4500$ in 6 days = 22500$in 30 days Re: If 5 men with 7 boys can earn 3825$ in 6 days and 2 men with 3 boys ca &nbs [#permalink] 23 Jul 2018, 05:25
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