Unitary Method Problem

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[email protected]: Junior | Next Rank: 30 Posts; Posts: 11; Joined: Sat Oct 10, 2015 12:42 am; Thanked: 1 times

by [email protected] » Sat Oct 10, 2015 12:45 am

15 labourers can fill 35 boxes in 7 days. How many labourers can fill 65 boxes in 5 days ?

(a) 13

(b) 39

(c) 45

(d) 65

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Source: Beat The GMAT — Problem Solving | Sat Oct 10, 2015 12:45 am

GMATGuruNY: GMAT Instructor; Posts: 15539; Joined: Tue May 25, 2010 12:04 pmFollowed by: 1906 members; Location: New York, NY; Thanked: 13060 times; GMAT Score:790

by GMATGuruNY » Sat Oct 10, 2015 1:18 am

[email protected] wrote:15 labourers can fill 35 boxes in 7 days. How many labourers can fill 65 boxes in 5 days ?

(a) 13

(b) 39

(c) 45

(d) 65

Use the following formula:

(workers * time)/(output) = (workers * time)/(output)

Since 15 workers require 7 days to fill 35 boxes, and we must determine how many workers in 5 days can fill 65 boxes, we get:

(15 * 7)/35 = (x * 5)/65
3 = x/13
x = 39.

The correct answer is B.

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theCEO: Master | Next Rank: 500 Posts; Posts: 363; Joined: Sun Oct 17, 2010 3:24 pmFollowed by: 3 members; Thanked: 115 times

by theCEO » Sat Oct 10, 2015 1:19 am

[email protected] wrote:15 labourers can fill 35 boxes in 7 days. How many labourers can fill 65 boxes in 5 days ?

(a) 13

(b) 39

(c) 45

(d) 65

There are 3 items. The key is to change the 2 items at once and leave the other constant.

07days ..... 15men ..... 35boxes
01days ..... 15men ..... 05boxes
here we changed the ratio of days and boxes and kept men constant

01days ..... 15men ..... 05boxes
13days ..... 15men ..... 65boxes
here we changed the ratio of days and boxes and kept men constant

13days ..... 15men ..... 65boxes
13days x (5/13) ..... 15men x (13/5) ..... 65boxes
if we decrease the number of days by x, we have to decrease the number of men by 1/x

13days x (5/13) ..... 15men x (13/5) ..... 65boxes
5days ..... 39men ..... 65boxes

ans = b

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