IIFT 2020 Question 9

Question 9

Surojit Ghosh left his IT job last year and started a food business with his wife Debjani. They named
the business "Bong's Kitchen". Surojit takes $$4\frac{1}{5}$$ hours more when he works alone compared to when
he works jointly with his wife. On the other hand, Debjani takes $$28\frac{1}{5}$$ hours more than what she takes
when she works with Surojit. How long approximately will it take, Surojit to complete the business
work alone ?


Let the number of hours needed by Surojit working alone be S hours and the number of hours required by Debjani when she works alone be D. 
The time required to finish the work when they work together = $$\frac{S\cdot D}{S+D}$$

Hence, we can frame the given 2 conditions as: 
$$S-\frac{S\cdot D}{S+D}=\frac{21}{5}$$ ............(1)
$$D-\frac{S\cdot D}{S+D}=\frac{141}{5}$$ ..........(2) 

Solving the two equations simultaneously, we get S = 15 hours approx

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