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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 44 days if they all work together for 88 hours per day. However, Anu and Tanu work together for the first 66 days, working 66 hours 4040 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is

Entered answer:

Solution

✅ Correct Answer: 6

We have three workers with different speeds, and we need to find how long one of them takes to finish remaining work.

Given Information:

Time ratio for Anu : Tanu : Manu = 5 : 8 : 10

Working together, they can complete the job in 4 days (8 hours/day)

Anu and Tanu work together for 6 days (6 hours 40 minutes/day)

Find: Hours needed for Manu to complete remaining work


If time ratios are 5:8:10, then work rate ratios are 15:18:110\frac{1}{5} : \frac{1}{8} : \frac{1}{10}

Let's assume individual times are 5k, 8k, and 10k hours respectively.

Work rates (efficiency):

Anu's rate = 15k\frac{1}{5k} units per hour

Tanu's rate = 18k\frac{1}{8k} units per hour

Manu's rate = 110k\frac{1}{10k} units per hour

Using LCM helps us work with whole numbers instead of fractions, making calculations easier.

LCM of 5k, 8k, 10k = 40k

So if total work = 40k units:

Anu completes 40k÷5k=840k ÷ 5k = 8 units per hour

Tanu completes 40k÷8k=540k ÷ 8k = 5 units per hour

Manu completes 40k÷10k=440k ÷ 10k = 4 units per hour


Combined rate = 8+5+4=178 + 5 + 4 = 17 units per hour

Together they finish in 4×8=324 \times 8 = 32 hours

Total work = 17×32=54417 \times 32 = 544 units

Therefore: 40k=54440k = 544, so k=13.6k = 13.6


Time conversion: 66 hours 4040 minutes = 6+40606 + \frac{40}{60}

=6+23= 6 + \frac{2}{3}

=203= \frac{20}{3} hours

Work done by Anu and Tanu together:

Combined rate = 8+5=138 + 5 = 13 units per hour

Time worked = 6×203=406 \times \frac{20}{3} = 40 hours

Work completed = 13×40=52013 \times 40 = 520 units


Remaining work = 544−520=24544 - 520 = 24 units

Manu's rate = 44 units per hour

Time needed = 244=6\frac{24}{4} = 6 hours


Answer: 6

In work problems, we convert time ratios to rate ratios (reciprocals), use LCM for easier calculations, and always verify our answer makes sense with the given constraints.

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