Sanjay and Rahul working alone can do a piece of work in 80 days and 240 days. Sanjay and Rahul start working together on that work but after having worked for 20 days the work is increased. The additional work is such that Rahul would take 80 days alone to complete it. In order to cope with the additional load they called Nitesh and the remaining work is finished in 10 days.Find the number of days Nitesh alone would take to complete the original work.

1) 16
2) 12
3) 10
4) 18

• Sanjay and Rahul working alone can do a piece of work in 80 days and 240 days.so together they work in 1day=(1/80 + 1/240)=4/240=1/60.here they worked together for 20 days, so the work done in 20 days is 1/60*20=1/3.so remaining work after 20 days=(1-1/3)=2/3.now the work is increased. The additional work is such that Rahul would take 80 days alone to complete it.so the additional work is (1/240 *80)=1/3. so total work is (2/3+1/3)=1.they called Nitesh and the remaining work is finished in 10 days.so the 3 together work in 1 day 1/10 and sanjay and rahul together work in 1 day 1/60.so nitesh work in 1 day(1/10 - 1/60)=5/60.Nitesh alone would take to complete the original work =1/(5/60)=60/5=12
  The answer is 12
  
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