Time and Work Ratio

CAT 2022 Slot 2 · QA · Medium · Arithmetic

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Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5:8:105 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is

Answer

6

Explanation

Ratio of times taken by Anu, Tanu, Manu = 5:8:105 : 8 : 10. Let the time taken alone be 5t,8t,10t5t, 8t, 10t hours. Efficiencies are proportional to 15t,18t,110t\frac{1}{5t}, \frac{1}{8t}, \frac{1}{10t}. Taking LCM of 5, 8, 10 = 40 units total work rate multiplier. Efficiencies: Anu = 8 units/hr, Tanu = 5 units/hr, Manu = 4 units/hr. Combined efficiency = 8+5+4=178 + 5 + 4 = 17 units/hr. Total work required = 4 days×8 hrs/day×17=32×17=5444 \text{ days} \times 8 \text{ hrs/day} \times 17 = 32 \times 17 = 544 units. Anu and Tanu work for 6 days at 6 hrs 40 mins=2036 \text{ hrs } 40 \text{ mins} = \frac{20}{3} hours/day. Total hours worked by Anu and Tanu = 6×203=406 \times \frac{20}{3} = 40 hours. Work done by Anu and Tanu = 40 hrs×(8+5)=40×13=52040 \text{ hrs} \times (8 + 5) = 40 \times 13 = 520 units. Remaining work = 544−520=24544 - 520 = 24 units. Time taken by Manu alone = 244=6\frac{24}{4} = 6 hours.

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