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P can do a work in 24 days, while Q do it in 36 days. P and Q worked for alternate turns (started with P), such that on first turn P worked for one day, on second turn Q worked for 2 days and on third turn P worked for 3 days and so on. Find the time taken by R alone to complete the work which is sum of thrice the work done by P in 10 turns and six times of work done by Q in his 10 turns, if R is 20% more efficient than combined efficiency of P and Q together?
  • a)
    225 days
  • b)
    175 days
  • c)
    185 days
  • d)
    205 days
  • e)
    None of these
Correct answer is option 'E'. Can you explain this answer?
Most Upvoted Answer
P can do a work in 24 days, while Q do it in 36 days. P and Q worked ...
Ratio of time taken by P and Q alone to complete the work = 24: 36 =2:3
Ratio of efficiency of P and Q = 3: 2 [3a and 2a]
Amount of work done by P in his 10 turns = 3a x [1 + 3 + 5…………. up to 10 terms] = 3a x 102 = 300a
Amount of work done by Q in his 10 turns = 2a x [2 + 4 + 6……. 10 terms = 2a x 10 x 11 = 220a
So total work, to be done by R = 3 x 300a + 6 x 220a = 2220a
Efficiency of R = 120% x (2a + 3a) = 6a
Required time = 2220a/6a = 370 days
Hence answer is option E
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Community Answer
P can do a work in 24 days, while Q do it in 36 days. P and Q worked ...
Solution:

Calculating the work done by P and Q in 10 turns:
- In 10 turns, P works for 1 + 3 + 5 + 7 + 9 + 11 + 13 + 15 + 17 + 19 = 100 days
- In 10 turns, Q works for 2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 100 days

Calculating the efficiency of R:
- Let the efficiency of R be x, then the efficiency of P is 1/24 and the efficiency of Q is 1/36
- Combined efficiency of P and Q = 1/24 + 1/36 = 5/72
- Efficiency of R = 1.2 * (5/72) = 1.2 * 5/72 = 1/12

Calculating the time taken by R to complete the work:
- Work done by P in 10 turns = 100 days
- Work done by Q in 10 turns = 100 days
- Total work done by R in 10 turns = 3 * 100 + 6 * 100 = 900 days
- As efficiency of R is 1/12, time taken by R to complete the work = 900 * 12 = 10800 days
Therefore, the time taken by R alone to complete the work is 10800 days, which is not listed in the options provided. Hence, the correct answer is none of these (option E).
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P can do a work in 24 days, while Q do it in 36 days. P and Q worked for alternate turns (started with P), such that on first turn P worked for one day, on second turn Q worked for 2 days and on third turn P worked for 3 days and so on. Find the time taken by R alone to complete the work which is sum of thrice the work done by P in 10 turns and six times of work done by Q in his 10 turns, if R is 20% more efficient than combined efficiency of P and Q together?a)225 daysb)175 daysc)185 daysd)205 dayse)None of theseCorrect answer is option 'E'. Can you explain this answer?
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