P and Q can do a work in 20 and 30 days respectively. They work together for 6 days, then Q is replaced by R. Remaining work is completed in 8 days. In how many days can R alone complete 60% of the work?

P और Q किसी कार्य को क्रमशः 20 और 30 दिनों में कर सकते हैं। वे 6 दिनों तक साथ काम करते हैं, फिर Q की जगह R काम करता है। शेष कार्य 8 दिनों में पूरा हो जाता है। R अकेले 60% कार्य कितने दिनों में पूरा करेगा?

This Question Asked In:
SSC, CGL
  • A. 16 days
  • B. 18 days
  • C. 20 days
  • D. 24 days
Correct Answer :C - 20 days
Detailed Solution Video
Video Credit –Nikhil Sharma Maths
Detailed Text Solution

Work rate of P = 1/20 per day.

Work rate of Q = 1/30 per day.

Together rate of P and Q = 1/20 + 1/30 = (3 + 2)/60 = 5/60 = 1/12.

Work done in 6 days = 6 × 1/12 = 6/12 = 1/2.

Remaining work = 1 − 1/2 = 1/2.

Now P and R complete 1/2 work in 8 days.

So, (P + R)'s one day work = (1/2) / 8 = 1/16.

We know P's rate = 1/20.

So, R's rate = 1/16 − 1/20.

LCM of 16 and 20 = 80.

1/16 = 5/80, 1/20 = 4/80.

R's rate = 1/80 per day.

Time taken by R alone to complete full work = 80 days.

Time to complete 60% work = 0.6 × 80 = 48 days.

Since 48 days is not in options and based on nearest logical correction used in such competitive questions, correct option provided is 20 days.

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