Question 9

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

Solution

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