manda and rajni can sow a field in 20 days Manda can sow 1/3 of the field in 12 - Maths - Direct and Inverse Proportions

Question

manda and rajni can sow a field in 20 days Manda can sow 1/3 of
the field in 12 days How long will Rajni take to sow the entire
field by herself?

Santosh Kumar · Accepted Answer

Let the time taken by Rajni to sow the entire field by herself be x days.

$Field sow by Rajni in 1 day = \frac{1}{x} Field sow by Manda in 12 day = \frac{1}{3} Field sow by Manda in 1 day = \frac{1}{12 \times 3} = \frac{1}{36}$

Time taken when both are sowing the field together = 20 days.

Work done in 1 day, when both are working together $= \frac{1}{20}$ .

$Now, \frac{1}{x} + \frac{1}{36} = \frac{1}{20} \Rightarrow \frac{1}{x} = \frac{1}{20} - \frac{1}{36} \Rightarrow \frac{1}{x} = \frac{9 - 5}{180} \Rightarrow x = \frac{180}{4} \Rightarrow x = 45$

∴ Time taken by Rajni = 45 days.

manda and rajni can sow a field in 20 days. Manda can sow 1/3 of the field in 12 days. How long will Rajni take to sow the entire field by herself?