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Retired Moderator
Joined: 16 Apr 2020
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Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
If 6 men and 4 boys can reap 24 acres in 3 days,
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18 Feb 2021, 01:52
18 Feb 2021, 01:52
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Question Stats:
80% (02:41) correct
20% (03:49) wrong based on 5 sessions
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If 6 men and 4 boys can reap 24 acres in 3 days, while 2 men and 3 boys can reap 18 acres in 6 days, how many boys must assist 8 men in order to reap 44 acres in 4 days?
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Retired Moderator
Joined: 16 Apr 2020
Status:Founder & Quant Trainer
Affiliations: Prepster Education
Posts: 1546
Given Kudos: 172
Location: India
WE:Education (Education)
If 6 men and 4 boys can reap 24 acres in 3 days,
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19 Feb 2021, 02:11
19 Feb 2021, 02:11
1
OA Explanation
When we have a comparison between Men, Time and Work, Use:
M1 x T1 x W2 = M2 x T2 x W1
Here,
M1 = (6M + 4B)
T1 = 3
W1 = 24
M2 = (2M + 3B)
T2 = 6
W2 = 18
M3 = (8M + xB)
T3 = 4
W3 = 44
So,
\(\frac{(6M + 4B)(3)}{24} = \frac{(2M + 3B)(6)}{18}\)
\(18M + 12B = 16M + 24B\)
\(2M = 12B\)
\(M = 6B\)
Now, we can equate the third case with any of one of the two;
\(\frac{(2M + 3B)(6)}{18} = \frac{(8M + xB)(4)}{44}\)
\(\frac{(2M + 3B)}{3} = \frac{(8M + xB)}{11}\)
Plug \(M = 6B\) in the above equation:
\(\frac{(12B + 3B)}{3} = \frac{(48B + xB)}{11}\)
\(\frac{15B}{3} = \frac{(48 + x)B}{11}\)
\(5 = \frac{(48 + x)}{11}\)
\(55 = (48 + x)\)
\(55 - 48 = x\)
\(x = 7\)
Hence, 7 boys must assist those 8 men
When we have a comparison between Men, Time and Work, Use:
M1 x T1 x W2 = M2 x T2 x W1
Here,
M1 = (6M + 4B)
T1 = 3
W1 = 24
M2 = (2M + 3B)
T2 = 6
W2 = 18
M3 = (8M + xB)
T3 = 4
W3 = 44
So,
\(\frac{(6M + 4B)(3)}{24} = \frac{(2M + 3B)(6)}{18}\)
\(18M + 12B = 16M + 24B\)
\(2M = 12B\)
\(M = 6B\)
Now, we can equate the third case with any of one of the two;
\(\frac{(2M + 3B)(6)}{18} = \frac{(8M + xB)(4)}{44}\)
\(\frac{(2M + 3B)}{3} = \frac{(8M + xB)}{11}\)
Plug \(M = 6B\) in the above equation:
\(\frac{(12B + 3B)}{3} = \frac{(48B + xB)}{11}\)
\(\frac{15B}{3} = \frac{(48 + x)B}{11}\)
\(5 = \frac{(48 + x)}{11}\)
\(55 = (48 + x)\)
\(55 - 48 = x\)
\(x = 7\)
Hence, 7 boys must assist those 8 men
Re: If 6 men and 4 boys can reap 24 acres in 3 days,
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27 Feb 2021, 05:35
27 Feb 2021, 05:35
Solution:
Let the men be M and Boys be B
Thus, we get
6M+4B=24 Acres (in 3 days)
i.e.6M+4B=8 Acres(in 1 day)..................(1)
2M+4B=18 (in 6 days)
2M+4B=3 (in 1 day)...................(2)
Adding eqn 1 & 2
6M+4B=8
2M+3B=3
------------
8M+7B=11.....(in 1 day)
Therefore, 8M+7B=44 Acres (in 4 Days)
And the number of boys required=7
Answer=7
Hope this helps!
Let the men be M and Boys be B
Thus, we get
6M+4B=24 Acres (in 3 days)
i.e.6M+4B=8 Acres(in 1 day)..................(1)
2M+4B=18 (in 6 days)
2M+4B=3 (in 1 day)...................(2)
Adding eqn 1 & 2
6M+4B=8
2M+3B=3
------------
8M+7B=11.....(in 1 day)
Therefore, 8M+7B=44 Acres (in 4 Days)
And the number of boys required=7
Answer=7
Hope this helps!
