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, t

Question

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:

Accepted Answer

6 — Easy Convert the time ratio into an efficiency (work-per-hour) ratio by inverting it. Find the total work from the "all three for $4$ days $	imes$ $8$ h" condition, subtract what Anu and Tanu do in $6$ days, and let Manu mop up the rest. 1 Efficiencies are reciprocals of times $5:8:10$: $$\frac15:\frac18:\frac1{10}=8:5:4 \quad(	ext{multiply by LCM }40).$$ Let efficiencies be $8x,5x,4x$ units per hour. 2 Total work (all three, $4$ days, $8$ h/day): $$(8x+5x+4x)	imes4	imes8=17x	imes32=544x.$$

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