20 workers can reap a field in 30 days. If after every 10 days, 20 more workers are employed, in how many days shall the whole field be reaped?
Solution
Correct Answer: Option D
20 workers can reap a field 30 days.
∴ Part of field reaped by 20 workers in 1 day = 1/30
⇒ Part of field reaped by 1 worker in 1 day = \(\frac{1}{{20 \times 30}}\)
⇒ Part of field reaped by 20 workers in 10 days \(= \;\frac{{20 \times 10}}{{20 \times 30}} = \frac{1}{3}\)
∴ In the first 10 days 20 workers have reaped \(\frac{1}{3}\)rd part of the field.
At the end of 10 days 20 more workers have been employed. Therefore for the next span of 10 days the number of workers working are 20 + 20 = 40.
∴ in the next 10 days: part of filed reaped by 40 workers \(= \;\frac{{40 \times 10}}{{20 \times 30}} = \frac{2}{3}\)
⇒ part of field reapedafter 20 days = part reaped in first 10 days + part reaped in next 10 days
⇒ Part of field reaped after 20 days = (1/3) + (2/3) = 1
∴ the entire field gets reaped by the end of 20 days.
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