1.

A, B and C can complete a work in 20, 24 and 30 days respectively. All three of them starts together but after 4 days A leaves the job and B left the job 6 days before the work was completed. C completed the remaining work alone. In how many days was the total work completed?1). 102). 123). 144). 16

Answer»

LET the total amount of work be X

Work done by A is one day = X/20

Work done by B in one day = X/24

Work done by C in one day = X/30

A, B and C work together for 4 days, Work finished in four days = 4 × ((X/20) + (X/24) + (X/30)) = 4 × (6 + 5 + 4) × X / 120

This give the work finished in first four days = (1/2) × X

B left the job 6 days before the work was finished, so C worked alone for 6 days

Work done by C in 6 days is = 6 × X / 30 = X/5

Work done by (X/2) + (X/5) = (7 × X)/10

Work left = X - (7/10) × X = (3/10) × X

This work is finished by B and C working together

The work done by B and C in one day is = (X/24) + (X/30) = (9/120) × X

Let B and C together work for N days then

N × (9/120) × X = (3/10) × X

This means N = 4

∴ Total number of days = 4 + 4 + 6 = 14


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