Question

Neena, Meena and Tina can do a piece of work in 4 days, 8 days and 6 days respectively. Neena and Tina work together for 1 day and then Neena leaves and Tina is joined by Meena to complete the work. How long does Tina work(in hours)?

Answer 1

Hint: We have to get knowledge of ratio and proportion. Now we have to calculate the one-day work of everyone. Then we are going to use the ratio and proportion method to determine Tina's one-day work.

Complete step-by-step answer:
Neena can do a piece of work in 4 days.
Meena can do a piece of work in 8 days.
Tina can do a piece of work in 6 days.
Let’s assume total work be 1.
Now calculate the one-day work of Neena, Meena, and Tina.
Neena’s one-day work = 1/4.
Meena’s one-day work = 1/8.
Tina’s one-day work = 1/6.
We have to calculate the work done by the Neena and Tina in 1 day is,
$\begin{align}
\Rightarrow & \dfrac{1}{4}+\dfrac{1}{6}=\dfrac{6+4}{24} \\
 & =\dfrac{5}{12}
\end{align}$
The work left after Neena and Tina work for 1 day is,
$\begin{align}
\Rightarrow & 1-\dfrac{5}{12}=\dfrac{12-5}{12} \\
 & =\dfrac{7}{12}
\end{align}$
We have to Calculate the work done by Meena and Tina in 1 day is,
$\begin{align}
\Rightarrow & \dfrac{1}{8}+\dfrac{1}{6}=\dfrac{8+6}{48} \\
 & =\dfrac{7}{24}
\end{align}$
If Meena and Tina can do 7/24 of work in 1 day.
So time taken by Meena and Tina to complete 7/12 of work in x days. So,
$\begin{align}
  & \dfrac{7}{24}x=\dfrac{7}{12} \\
 & \dfrac{x}{2}=1 \\
\Rightarrow & x=2
\end{align}$
That’s by total time taken by Tina is 2 days with Meena and 1 day with Neena.
So the total time taken by Tina is 3 days.
So we have to determine the total time taken in hours is,
$3\times(24)= 72$ , Therefore Tina takes 72 Hours to complete the work.

Note: We have to be careful during the calculation of total time taken by Meena and Tina. During the calculation of Tina’s one-day work using ratio and proportion we have to be careful and also at the time of conversion of days in hour.