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A can complete a work in 16 days, working 6 hours a day. B can complete the same work in 12 days, working 9 hours a day. If both A and B work together, working 8 hours a day, in how many days can they complete the work?

Solution

✅ Correct Option: 1

A can complete the work in 16 days, working 6 hours a day.

Total hours A needs to complete the work:

16×616 \times 6

=96= 96 hours


B can complete the work in 12 days, working 9 hours a day.

Total hours B needs to complete the work:

12×912 \times 9

=108= 108 hours


A completes 196\dfrac{1}{96} of the work in 1 hour.

B completes 1108\dfrac{1}{108} of the work in 1 hour.

Together in 1 hour:

196+1108\dfrac{1}{96} + \dfrac{1}{108}

Finding LCM of 96 and 108:

LCM =864= 864

196=9864\dfrac{1}{96} = \dfrac{9}{864}

1108=8864\dfrac{1}{108} = \dfrac{8}{864}

9864+8864\dfrac{9}{864} + \dfrac{8}{864}

=17864= \dfrac{17}{864} of the work per hour


Working 8 hours a day together, work completed in 1 day:

8×178648 \times \dfrac{17}{864}

=136864= \dfrac{136}{864}

=17108= \dfrac{17}{108} of the work


Total days needed to complete the work:

1÷171081 \div \dfrac{17}{108}

=1×10817= 1 \times \dfrac{108}{17}

=10817= \dfrac{108}{17} days

Therefore, they can complete the work in 10817\dfrac{108}{17} days.

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