Question
A and B together can finish a job in ‘x’ days, while
A alone takes ‘x + 32’ days to complete it. B alone can finish the job in 90 days. If C is 20% more efficient than A, how many days will C alone take to complete the work?Solution
According to question;
1/(x + 32) + 1/90 = 1/x
Or, x² + 122x = 90x + 2880
Or, x² + 32x – 2880 = 0
Or, x² + 72x – 40x – 2880 = 0
Or, x(x + 72) – 40(x + 72) = 0
Or, (x – 40)(x + 72) = 0
So, x = 40, -72
Number of days can’t be negative, so x = 40
Time taken by A to complete the work = 40 + 32 =72 days
Total work = 360 units (LCM of 40 and 72)
Efficiency of A = 360/72 = 5 units per day
Efficiency of C = 1.20 × 5 = 6 units per day
Desired time = 360/6 = 60 days
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