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Reena, Aastha and Shloka can independently complete a piece of work in 6 hours, 4 hours and 12 hours respectively. If they work together, how much time will they take to complete that piece of work ?
Answer & Solution
Correct Answer:
Option
A
$$\eqalign{
& {\text{Reena's 1 hour's work}} = \frac{1}{6}{\text{ }} \cr
& {\text{Aastha's 1 hour's work}} = \frac{1}{4}{\text{ }} \cr
& {\text{Shloka's 1 hour's work}} = \frac{1}{{12}}{\text{ }} \cr} $$
( Reena + Aastha + Shloka )'s 1 hour's work
$$\eqalign{ & = \frac{1}{4} + \frac{1}{6}{\text{ + }}\frac{1}{{12}} \cr & {\text{ = }}\frac{6}{{12}} \cr & = \frac{1}{2} \cr} $$
Hence, Reema, Aastha and Shloka together take 2 hours to complete the work.
( Reena + Aastha + Shloka )'s 1 hour's work
$$\eqalign{ & = \frac{1}{4} + \frac{1}{6}{\text{ + }}\frac{1}{{12}} \cr & {\text{ = }}\frac{6}{{12}} \cr & = \frac{1}{2} \cr} $$
Hence, Reema, Aastha and Shloka together take 2 hours to complete the work.
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