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

Answer 1

Correct Answer: 6

Times taken are in ratio:

\[ Anu : Tanu : Manu = 5 : 8 : 10 \]

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

Individual rates:

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

Together, rate = \(8 + 5 + 4 = 17\) units/hr. They finish job in 32 hours:

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

Anu and Tanu work for 6 days, 6 hours and 40 minutes per day (\(=\frac{20}{3}\) hours):

\[ \text{Total hours} = 6 \times \frac{20}{3} = 40. \]

Work done by Anu and Tanu:

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

Remaining work:

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

Time Manu takes (\(y\)) to finish remaining work at 4 units/hr:

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

Final Answer:

Manu will take 6 hours to complete the remaining job.

Answer 2

Given time ratios:

\[ Anu : Tanu : Manu = 5 : 8 : 10 \]

Efficiencies (units per hour) are inverse of times (assuming total work = \(40x\)):

\[ 8 : 5 : 4 \]

Total efficiency:

\[ 8 + 5 + 4 = 17 \text{ units/hr} \]

Total time when all work together:

\[ 8 \text{ hours/day} \times 4 \text{ days} = 32 \text{ hours} \]

Total work completed:

\[ 40x = 17 \times 32 = 544 \]

Anu and Tanu work for 6 days, 6 hours 40 minutes/day = \( \frac{20}{3} \) hours/day:

\[ 6 \times \frac{20}{3} = 40 \text{ hours} \]

Work done by Anu and Tanu:

\[ (8 + 5) \times 40 = 13 \times 40 = 520 \]

Remaining work:

\[ 544 - 520 = 24 \]

Manu's rate is 4 units/hr, so time taken to finish remaining work:

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

Answer: Manu will take 6 hours to complete the remaining job alone.