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Nitu and nitika plan to finish a work in 10 days. They start working together. But after 7days they found that only half of the work was done. So they took help of naveen who is as efficient as nitika. In how many days will they finish the work if nitu is 1.5 times as efficient as nitika?
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It will take another 5 days therefore the original 7 days plus a further 5 = 12 days total.

Together Nitu and Nitika complete half the work in 7 days
Therefore together they would finish the work in 14 days (2 * 7)
Substituting Nitu with 1.5 Nitika it means that (1.5 + 1 = 2.5) Nitikas could finish the job in 14 days

By himself only Nitika could therefore finish the job in 14 * 2.5 = 35 days
Naveen by himself could also finish the job in 35 days
Nitu could finish the job in 35 * 2/3 = 70/3 days 23 1/3 days

Therefore as the LCM of 35 and 23 1/3 = 70
In seventy days Working together they could complete 70/35 + 70/35 + 70/23 1/3 jobs
= 2 + 2 + 3 = 7 jobs completed in 70 days
1 job therefore takes 70 /7 = 10 days

As half the work has already been completed before Naveen starts, the job will be finished in 10 / 2 = 5 days

CHECK
In 5 days Nitika can complete 5/35 of the work = 10/70
In 5 days Naveen can complete 5/35 of the work =10/70
In 5 days Nitu can complete 5/ 23 1/3 of the work = 15/70
in 5 days working together they can complete 10/70 + 10/70 + 15/70 = 35/70 = 1/2 the work

In the 7 days before taking on Naveen, Nitu will have completed 7 / (23 1/3) of the work = 21/70
Nitika will have completed 7/35 = 14/70 of the work
21/70 + 14/70 = 35/70 = 1/2 therefore CORRECT


ANSWER = another 5 DAYS with the three working together + the original 7 days taken by Nitu and Nitika = 12 days altogether

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