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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

Updated On: Jan 15, 2026
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Correct Answer: 6

Solution and Explanation

The time taken by Anu, Tanu, and Manu is in the ratio \( 5 : 8 : 10 \).

Let their respective times be \(5x, 8x, 10x\). The total work is \(W = 40x\) units.

Their individual rates are:

\[ \text{Anu's rate} = \frac{W}{5x} = 8, \quad \text{Tanu's rate} = \frac{W}{8x} = 5, \quad \text{Manu's rate} = \frac{W}{10x} = 4. \]

Their combined rate is \(8 + 5 + 4 = 17\) units/hr. They complete the job in 32 hours, so:

\[ 40x = 17 \times 32 \implies x = 13.6. \]

Anu and Tanu work for 6 days, for 6 hours and 40 minutes each day. This is \(6 \times \frac{20}{3}\) hours per day.

\[ \text{Total hours worked by Anu and Tanu} = 6 \times \frac{20}{3} = 40 \text{ hours}. \]

The work done by Anu and Tanu together is:

\[ (8 + 5) \times 40 = 13 \times 40 = 520 \text{ units}. \]

The remaining work is:

\[ 40x - 520 = 544 - 520 = 24 \text{ units}. \]

Let \(y\) be the time Manu takes to complete the remaining work at his rate of 4 units/hr:

\[ 4y = 24 \implies y = 6 \text{ hours}. \]

Final Answer:

Manu will take 6 hours to complete the remaining job.

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