Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 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:
Explanation:
Ratio of time taken by Anu, Tanu and Manu is 5 : 8 : 10. ⇒ Ratio of efficiencies of Anu, Tanu and Manu = 15 : 18 : 110 = 8 : 5 : 4 Let their efficiencies be 8x, 5x and 4x respectively per hour.
Total work done by them in 4 days = (8x + 5x + 4x) × 4 × 8 = 17x × 32 = 544x
Now, Anu and Tanu worked by 6 days working 6 hours 40 minute i.e., 623 hours daily. ∴ Worked completed by Anu and Tanu = 13x × 6 × 203 = 520x
⇒ Time taken by Manu to complete the remaining work = 544x-520x4x = 6 hours.
Hence, 6.
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