Kumar completes a work in 8 days and Raj completes the same work in 16 days. In how many days can Kumar and Raj together complete the work?
$3 rac{1}{3}$ days
$5 rac{1}{3}$ days
$1 rac{1}{3}$ days
$ rac{1}{3}$ day
Answer is Right!
Answer is Wrong!
This question was previously asked in
UPSC CBI DSP LDCE – 2023
Raj completes the work in 16 days, so his work rate is $\frac{1}{16}$ of the work per day.
When working together, their work rates add up.
Combined work rate = Work rate of Kumar + Work rate of Raj
Combined work rate = $\frac{1}{8} + \frac{1}{16}$ per day.
To add the fractions, find a common denominator, which is 16.
Combined work rate = $\frac{2}{16} + \frac{1}{16} = \frac{3}{16}$ of the work per day.
The time taken to complete the work together is the reciprocal of the combined work rate.
Time taken together = $\frac{1}{\text{Combined work rate}} = \frac{1}{\frac{3}{16}} = \frac{16}{3}$ days.
Converting the improper fraction to a mixed number: $\frac{16}{3} = 5$ with a remainder of 1, so $5\frac{1}{3}$ days.
$\frac{1}{T} = \frac{1}{8} + \frac{1}{16} = \frac{2+1}{16} = \frac{3}{16}$.
$T = \frac{16}{3} = 5\frac{1}{3}$ days.