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Unitary Method Problem

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by [email protected] » Sat Oct 10, 2015 1:36 am
If 5 men working for 6 hours a day can reap a field in 20 days, in how many days will 15 men reap the field, working 8 hours a day ?

(a) 5 days

(b) 6 days

(c) 7 & 1/2 days

(d) 9 days
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by GMATGuruNY » Sat Oct 10, 2015 1:56 am
[email protected] wrote:If 5 men working for 6 hours a day can reap a field in 20 days, in how many days will 15 men reap the field, working 8 hours a day ?

(a) 5 days

(b) 6 days

(c) 7 & 1/2 days

(d) 9 days
Let the rate per worker = 1 unit per hour.
Rate for 5 men = 5 units per hour.
Work produced by 5 men working 6 hours per day = 5*6 = 30 units per day.
Work produced in 20 days = 20*30 = 600 units.
Thus, one field = 600 units.

Rate for 15 men = 15 units per hour.
Work produced by 15 men working 8 hours per day = 15*8 = 120 units per day.
At a rate of 120 units per day, the time required by 15 men to produce 600 units = 600/120 = 5 days.

The correct answer is A.
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by theCEO » Sat Oct 10, 2015 1:59 am
[email protected] wrote:If 5 men working for 6 hours a day can reap a field in 20 days, in how many days will 15 men reap the field, working 8 hours a day ?

(a) 5 days

(b) 6 days

(c) 7 & 1/2 days

(d) 9 days
only change 2 of the 3 items at once, keep the other variable constant.
05men ..... 6hr ..... 020days
05men ..... 1hr ..... 120days
05men ..... 8hr ..... 015days
15men ..... 8hr ..... 005days

ans= a
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by [email protected] » Sat Oct 10, 2015 2:01 am
Is there any other shortcut method for solving this problem ? This solution no doubt helped me but also confused me and can confuse in future which could hurt my score ?? So if any other simpler method ??
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by GMATGuruNY » Sat Oct 10, 2015 2:07 am
[email protected] wrote:Is there any other shortcut method for solving this problem ? This solution no doubt helped me but also confused me and can confuse in future which could hurt my score ?? So if any other simpler method ??
Use the following formula:

(workers)(hours)(days) = (workers)(hours)(days)

Since 5 men working 6 hours per day require 20 days, and we must determine how days are required by 15 men working 8 hours per day, we get:

5*6*20 = 15*8*x
2*20 = 8x
40 = 8x
x = 5.

The correct answer is A.
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