A can complete a work in 8 days and B can complete the same work in 11 days How long will they take ...........

Quantitative Aptitude (CPO) Time and work

A can complete a work in 8 days and B can complete the same work in 11 days. How long will they take, if both work together?

This questions was previously asked in

SSC CPO 10th Nov 2022 Shift 3

$$4\frac{12}{17}$$

$$5\frac{12}{19}$$

$$4\frac{11}{19}$$

$$4\frac{12}{19}$$

- A's Work Rate: A can finish the work in 8 days, so A does 1/8 of the work in a day.

- B's Work Rate: B can complete it in 11 days, so B does 1/11 of the work in a day.

- Combined Work Rate: Together, they can do 1/8 + 1/11 of the work each day.

- Calculation: (1/8 + 1/11) = (11/88 + 8/88) = 19/88. So, both together can complete 19/88 of the work in one day.

- Total Days Together: They will take the reciprocal of their combined daily work rate, which is 88/19 days.

- Convert to Mixed Fraction: 88/19 = 4 with a remainder of 12, so that’s 4 12/19 days.

- Correct Option: Option 4 - $4\frac{12}{19}$

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