Multiple choice

Prakash, Qasim, and Raunak can complete a task in 54 days together. Prakash and Qasim together can complete three times the work that Raunak can do in a day. Prakash and Raunak together can complete four times the work that Qasim can do in a day. Find the number of days it takes for Raunak to complete the work alone.

  1. 96 days

  2. 120 days

  3. 108 days

  4. 216 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let P, Q, R be work rates. P+Q+R = 1/54. P+Q = 3R. P+R = 4Q. From P+Q=3R, substitute into first: 3R+R = 1/54 => 4R = 1/54 => R = 1/216. Raunak takes 216 days.

AI explanation

Let Prakash, Qasim, and Raunak's daily work be P, Q, and R, making their combined daily work P + Q + R = 1/54. From the given ratios, P + Q = 3R and P + R = 4Q. Substituting these into the total work equation yields 3R + R = 1/54, meaning R = 1/216. Raunak alone completes the work in 216 days.

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