Multiple choice

Each of Selena, Rajavi and Priya needs a unique time to complete a piece of work. Selena takes 6 days less than the time taken by Rajavi to finish the same work. Both Selena and Rajavi together can finish it in 4 days and Priya takes 2 days more than the time taken by Selena to complete the same work. How many days will Rajavi take to complete the work?

  1. 8 days

  2. 10 days

  3. 13 days

  4. 12 days

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let Rajavi take R days. Selena takes R-6 days. Together: 1/R + 1/(R-6) = 1/4. Solving: (R-6+R)/(R(R-6)) = 1/4, so 4(2R-6) = R^2-6R, 8R-24 = R^2-6R, R^2-14R+24 = 0. (R-12)(R-2) = 0. Since R must be greater than 6, R = 12.

AI explanation

Using the work equivalence formula, the sum of their individual rates equals their combined rate: 1 over R plus the quantity 1 over R minus 6 equals 1 over 4. Multiplying by the least common multiple of 4R times the quantity R minus 6 gives 4R minus 24 plus 4R equals R squared minus 6R. This rearranges to the quadratic equation R squared minus 14R plus 24 equals 0. Factoring this equation gives the roots 2 and 12, and since Rajavi's time must be greater than 6 days, Rajavi takes 12 days to complete the work.

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