Question

At a Covid-19 testing laboratory, 8 technicians can test 560 samples in 36 hours. How long (in days) can 15 technicians test 525 samples?​

Answer 1

Each technician is testing 560/8 =70samples in 36hrs

Time taken by 1 technician to test 1 sample=36/70hrs

Now 525 samples are there

Technicians available=15

Samples covered by technicians in 1hr=70/36 ×15=1050/36

Time taken to test 525 =525×36/1050=18hrs

In days=18/24=3/4

Answer 2

Given,

$\textit{``\, 8 technicians can test 560 samples in 36 hours."}$

For a constant time interval, no. of technicians should be directly proportional to no. of samples tested, as more technicians can test more samples at the same time.

Let the constant of proportionality among no. of technicians and no. of samples be $x.$ Then,

$\longrightarrow8x=560$

$\longrightarrow x=70$

In case of 15 technicians,

$\longrightarrow 15x=1050$

Hence,

$\textit{``\, 15 technicians can test 1050 samples in 36 hours."}$

For a constant no. of technicians, the no. of samples tested should be directly proportional to the time taken, as the same no. of technicians can test more samples for more time.

Let the constant of proportionality among no. of samples and time taken be $y.$ Then,

$\longrightarrow 1050y=36$

$\longrightarrow y=\dfrac{6}{175}$

In case of 525 samples,

$\longrightarrow 525y=18$

Hence,

$\underline{\underline{\textit{``\, 15 technicians can test 525 samples in 18 hours, i.e., in \dfrac{3}{4} days."}}}$

Hence $\bf{18\ hours=\dfrac{3}{4}\ days}$ is the answer.