Time & Work Mcqs

Q.  If X and Y complete a certain work in 10 days, Y and Z in 16 days and X and Z in 22 days, find the time required for each one to complete the work while working separately.

a. 120, 40, 60 days
b. 120, 60, 80 days
c. 40, 30, 120 days
d. 30, 40, 60 days


ANSWER: See Answer
 
Let a: be the time in which X & Y completes their work = 30 days
b: time in which Y & Z completes their work = 24 days
c: time in which X & Z completes their work = 40 days
X alone can complete the work in (2 * a * c) / (ab + bc – ac) days
= 2 * 30 * 24 * 40 / ((30 * 24) + (24 * 40) – (30 * 40)) = 120 days
Y alone can complete the work in 2 * a * b * c / (- ab + bc + ac) days
= 2 * 30 * 24 * 40 / (-(30 * 24) + (24 * 40) + (30 * 40)) = 40 days
Z alone can complete the work in 2 * a * b * c / (ab – bc + ac) days
= 2 * 30 * 24 * 40 / ((30 * 24) – (24 * 40) + (30 * 40))
= 60 days
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