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If 5 men with 7 boys can earn 3825$ in 6 days and 2 men with 3 boys ca

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If 5 men with 7 boys can earn 3825$ in 6 days and 2 men with 3 boys ca  [#permalink]

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New post 18 Jul 2018, 01:32
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Question Stats:

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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
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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]

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New post 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
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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]

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New post 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.

Answer: 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]

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New post 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.

Answer: 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]

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New post 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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