Pooja and Ritu can do a piece of work in \[17\dfrac{1}{7}\] days. If one day work of Pooja be three fourth of one day work of Ritu; find in how many days each alone will do the work.
(a) Pooja in 40 days and Ritu in 30 days.
(b) Pooja in 60 days and Ritu in 40 days.
(c) Pooja in 30 days and Ritu in 10 days.
(d) Pooja in 45 days and Ritu in 20 days.

Hint: We solve this problem by assuming the number of days required for each of Pooja and Ritu as some variables. We use the two given conditions and solve for the two variables we assumed to get the answer. While applying the first condition we are not allowed to add the number of days instead we can convert the days to part of work in one day and apply the conditions.

Complete step by step answer:
Let us assume that Pooja takes \['x'\] days to finish the work alone.
Now, we can write that Pooja completes \[\dfrac{1}{x}\] part of work in one day.
Similarly, let us consider Ritu takes \['y'\] days to finish the work alone.
Now, we can write that Ritu completes \[\dfrac{1}{y}\] part of work in one day.
We are given that both Pooja and Ritu together complete the work in \[17\dfrac{1}{7}\] days.
Here, \[17\dfrac{1}{7}\] is the mixed fraction. So, by converting to proper fraction we get
 \[\begin{align}
  & \Rightarrow 17\dfrac{1}{7}=\dfrac{7\times 17+1}{7} \\
 & \Rightarrow 17\dfrac{1}{7}=\dfrac{120}{7} \\
\end{align}\]
So, Pooja and Ritu complete the work together in \[\dfrac{120}{7}\] days.
Now, we can write that Pooja and Ritu complete \[\dfrac{7}{120}\] part of work in one day.
By converting to mathematical equation we get
 \[\Rightarrow \dfrac{1}{x}+\dfrac{1}{y}=\dfrac{7}{120}.....equation\left( i \right)\]
We are given with the second condition that one day work of Pooja be three fourth of one day work of Ritu. By converting into mathematical equation we get
 \[\Rightarrow \dfrac{1}{x}=\left( \dfrac{3}{4} \right)\dfrac{1}{y}.....equation(ii)\]
Now, by substituting this equation (ii) in equation (i) we get
 \[\begin{align}
  & \Rightarrow \left( \dfrac{3}{4} \right)\dfrac{1}{y}+\dfrac{1}{y}=\dfrac{7}{120} \\
 & \Rightarrow \dfrac{1}{y}\left( \dfrac{3}{4}+1 \right)=\dfrac{7}{120} \\
 & \Rightarrow \dfrac{1}{y}\left( \dfrac{7}{4} \right)=\dfrac{7}{120} \\
 & \Rightarrow y=30 \\
\end{align}\]
Therefore Ritu completes the work alone in 30 days.
Now, by substituting the value of \['y'\] in equation (ii) we get
 \[\begin{align}
  & \Rightarrow \dfrac{1}{x}=\left[ \dfrac{3}{4} \right]\dfrac{1}{30} \\
 & \Rightarrow x=40 \\
\end{align}\]
Therefore Pooja completes the work alone in 40 days.

So, the correct answer is “Option a”.

Note: Students may make mistakes in taking the first condition. Here, we are not allowed to add the days when work of two people is combined. Students may make this mistake and consider \[x+y=\dfrac{120}{7}\] which gives the wrong answer. So, this part has to be taken care of and the remaining calculations also.