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RRB NTPC Graduate Tier 1 2016 Shift 2 📅 02 Apr, 2016

Working together, P, Q and R reap a field in 6 days. If P can do it alone in 10 days and Q in 24 days, in how many days will R alone be able to reap the field?

A
32 days
B
40 days
C
45 days
D
60 days
Result Summary
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APEDIA

RRB NTPC Graduate Tier 1
2016 • 02 Apr, 2016 • Shift 2
Working together, P, Q and R reap a field in 6 days. If P can do it alone in 10 days and Q in 24 days, in how many days will R alone be able to reap the field?
Correct Answer
40 days
Rate of Work formulation: Let the total work be 1 unit. The combined daily work rate of P, Q, and R is 1/6. P's daily rate is 1/10, and Q's daily rate is 1/24.E......
💡 Analysis & Explanation
Rate of Work formulation
Let the total work be 1 unit. The combined daily work rate of P, Q, and R is 1/6. P's daily rate is 1/10, and Q's daily rate is 1/24.
Equation Setup
The sum of their individual rates equals their combined rate: 1/P + 1/Q + 1/R = 1/6. Substituting the known values: 1/10 + 1/24 + 1/R = 1/6.
Solving for R
Rearranging gives 1/R = 1/6 - (1/10 + 1/24). The LCM of 6, 10, and 24 is 120.
Arithmetic Execution
1/R = 20/120 - (12/120 + 5/120) = 20/120 - 17/120 = 3/120 = 1/40.
Conclusion
R alone will take exactly 40 days to complete the work.