Question
Q can complete a project in ‘x ‘ hours , R needs
‘0.7x’ hours to do half of The same project. R and S jointly can complete the same project in 1/3 of time taken by Q to complete the work alone. Q takes 90 hours more to complete alone as compared to time taken by all three jointly to complete the work. Find the time taken by S to complete 80% of the project alone?Solution
Let time taken by R to finish work is – x hr, By Q is = 1.4x hr Therefore, R+S = (1.4x/3)hr So, by S alone work = [1/3/1.4x) – 1/x ] = 7x/8 hr Entire time taken by all together = (1.4x - 90)hr Therefore, 1/x + 1/1.4x + 8/7x = 1/1.4x-90 1.4x +1+1.6x/1.4x = 1/1.4x -90 5.6x -360 = 1.4x x = 600/7 Hence, time taken by S alone to complete 80% = 7/8 x 600/7 x 0.8 = 60 hrs
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