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# 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 will do the work alone?(a) Pooja in 44 days and Ritu in 8 days(b) Pooja in 80 days and Ritu in 500 days(c) Pooja in 20 days and Ritu in 120 days(d) Pooja in 40 days and Ritu in 30 days

Last updated date: 18th Mar 2023
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Hint: We solve this problem by using the fact by assuming that amount of work done by Pooja be $\dfrac{1}{a}$and the work done by Ritu be $\dfrac{1}{b}$(where a and b are the number of days required for Pooja and Ritu to do the work respectively). The trick is to assume work done to be inversely related to the number of days and then proceed with the problem to satisfy the necessary conditions.

We have,
$\dfrac{1}{a}+\dfrac{1}{b}=\dfrac{7}{120}$ -- (1)

To explain why work done should be inversely related to the number of days to complete the work, let us assume two cases. In the first case, Pooja takes 2 days to complete a work and in the second case, Pooja takes 5 days to complete a work. Clearly, the amount of work done in the first case is more since she was able to finish the same amount of work in less number of days. Thus, the amount of work done should be inversely related to the number of days to complete the task.

Thus, in this case, amount of work done is inversely proportional to $17\dfrac{1}{7}$, this is-

=$\dfrac{1}{17\dfrac{1}{7}}$

=$\dfrac{7}{120}$(as we have in (1))

Also, from second condition, we have,

$\dfrac{1}{a}=\dfrac{3}{4}\times \dfrac{1}{b}$ -- (2)

Putting value of (2) in (1), we get,

$\dfrac{3}{4b}+\dfrac{1}{b}=\dfrac{7}{120}$

$\dfrac{7}{4b}=\dfrac{7}{120}$

b=30

Also, from (2), we have,

$\dfrac{1}{a}=\dfrac{3}{4}\times \dfrac{1}{b}$

a=$\dfrac{4b}{3}$

a=$\dfrac{4\times 30}{3}$

a=40

Hence, Pooja takes 40 days and Ritu takes 30 days to complete the work alone respectively.

Hence, the correct answer is (d).

Note: While solving problems related to the calculating work done by a single person when work done by both people is given, we have to understand that the number of days required for 1 person to complete the work is more than the number of days required for both combined to complete the same work. Once we keep this in mind, we can easily solve the problem by using the inverse relation between work done and number of days required to complete the work.