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P and Q can do work separately in 10 and 20 days, respectively. In how many days can they finish it, working together?

Solution

✅ Correct Option: 2

P completes the work in 10 days.

P's rate =110= \frac{1}{10} work per day


Q completes the work in 20 days.

Q's rate =120= \frac{1}{20} work per day


When working together, their rates are added:

Combined rate =110+120= \frac{1}{10} + \frac{1}{20}

=220+120= \frac{2}{20} + \frac{1}{20}

=320= \frac{3}{20} work per day


To find the total days needed:

Days =Total WorkRate= \frac{\text{Total Work}}{\text{Rate}}

=1320= \frac{1}{\frac{3}{20}}

=1×203= 1 \times \frac{20}{3}

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

Therefore, P and Q working together can finish the work in 203\frac{20}{3} days.

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