Question 146
Dhiru can dig $$\frac{1}{a}$$ of a field in 20 hours. What fraction of the same field can Kaku dig in 20 hours if the two of them can dig the field in 60 hours, working together at their respective rates?
Solution
Dhiru can dig $$\frac{1}{a}$$ of a field in 20 hours.
=> Dhiru digs 1 part of field in $$20a$$ hours
Work done by Kaku = $$\frac{1}{60}-\frac{1}{20a}$$
= $$\frac{a-3}{60a}$$
$$\therefore$$ Part of field dug by Kaku in 1 hour = $$20\times\frac{(a-3)}{60a}$$
= $$\frac{(a-3)}{3a}$$
=> Ans - (D)
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