Multiple choice

Pooja and Ritu can do a piece of work in $\displaystyle 17\frac{1}{7}$ 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.

  1. Pooja in 40 days and Ritu in 30 days

  2. Pooja in 60 days and Ritu in 40 days

  3. Pooja in 30 days and Ritu in 10 days

  4. Pooja in 45 days and Ritu in 20 days
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A Correct answer
Explanation

Total work rate = 1 / (120/7) = 7/120 per day. Let Ritu's rate be R, then Pooja's is 3/4 R. R + 3/4 R = 7/120, so 7/4 R = 7/120, R = 1/30. Ritu takes 30 days. Pooja's rate = 3/4 * 1/30 = 1/40, so Pooja takes 40 days.

AI explanation

The combined one day work of Pooja and Ritu is 1 divided by (120 divided by 7), which equals 7 divided by 120. Let Ritu's one day work be x; then Pooja's one day work is (3 divided by 4)x. The sum of their one day works is x plus (3 divided by 4)x equals 7 divided by 120, so (7 divided by 4)x equals 7 divided by 120, yielding x equals 1 divided by 30. Ritu alone takes 30 days, and Pooja takes 1 divided by ((3 divided by 4) times (1 divided by 30)), which equals 40 days. Therefore, Pooja finishes it in 40 days and Ritu in 30 days.

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