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Pooja and Ritu can do a piece of work in $17 \frac{1}{7}$ days. If one day work of Pooja is three fourth of one day work of Ritu then find in how many days each alone will do the same work.

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Pooja in 40 days and Ritu in 30 days

Pooja in 60 days and Ritu in 40 days

Pooja in 30 days and Ritu in 10 days

Pooja in 45 days and Ritu in 20 days

answer is A.

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Detailed Solution

Given work done by Ritu and Pooja.
Let the work done by Pooja in one day be

\frac{1}{x}

and work done by Ritu in one day be

\frac{1}{y} .

Therefore, according to the question total work done by both in one day,

\frac{1}{x} + \frac{1}{y} = \frac{1}{17 \frac{1}{7}} = \frac{7}{120}

.....(1)
Also, one day work of Pooja is three fourth of one day work of Ritu,

\frac{1}{x} = \frac{3}{4} \times \frac{1}{y}

…………..(2)
Substituting above equation in equation (1), we get,

\frac{3}{4} \times \frac{1}{y} + \frac{1}{y} = \frac{7}{120}

\frac{7}{4 y} = \frac{7}{120}

y = 30

days
Substituting

y = 30

in equation (2) we get,

\frac{1}{x} = \frac{3}{4} \times \frac{1}{30}

x = 40

days
Hence Pooja will complete the work in

40

days whereas ritu in

30

days.
Therefore, option (1) is correct.

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