Latest Gate Aptitude Question SOLUTION: Five people A,B,C,D and E do a certain job . A, B and C together complete the job in 7.5 hrs ; A, C and E together complete it in 5 hrs; A, C and D together complete it in 6 hrs; B

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(#M40019795) GATE question tim work Keep an EYE

Five people A,B,C,D and E do a certain job . A, B and C together complete the job in 7.5 hrs ; A, C and E together complete it in 5 hrs; A, C and D together complete it in 6 hrs; B, D, and E together comple it in 4 hrs. If all te five people work together then how much time will be required to complete the job

Asked In Gate deepak (10 years ago)

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Vinay Sipani   (10 years ago)

In 1 day

In 1 hour,1/7.5 work is done which is equal to total work done by all in 1 hr
=> (1/A) + (1/B) + (1/C) = 1/7.5 --------------------(1)

similarly,
(1/A) + (1/C) + (1/E) = 1/5 -------------------------(2)
(1/A) + (1/C) + (1/D) = 1/6 -------------------------(3)
(1/B) + (1/D) + (1/E) = 1/4 -------------------------(4)

(1) + (2) + (3) + 2*(4)
=> 3A + 3B + 3C + 3D + 3E = (1/7.5) + (1/5) + (1/6) + 2*(1/4)
=> A + B + C + D + E = 1 day

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Vinay Sipani   (10 years ago)

In 3 hoursIn 1 hour,1/7.5 work is done which is equal to total work done by all in 1 hr=> (1/A) + (1/B) + (1/C) = 1/7.5 --------------------(1)similarly,(1/A) + (1/C) + (1/E) = 1/5 -------------------------(2)(1/A) + (1/C) + (1/D) = 1/6 -------------------------(3)(1/B) + (1/D) + (1/E) = 1/4 -------------------------(4)(1) + (2) + (3) + 2*(4) => 3/A + 3/B + 3/C + 3/D + 3/E = (1/7.5) + (1/5) + (1/6) + 2*(1/4)=> In 1 hour,1/A + 1/B 1/C + 1/D + 1/E = 1/3 work done

=> Total time taken = 3 hours

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srinivasulu b  (10 years ago)

2.2 hours

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