Ramesh and Rahman can do a work in 20 and 25 days respectively. After doing collectively 10 days of work, they leave the work due to illness and Suresh completes rest of the work in 3 days. How many days Suresh alone can take to complete the whole work ?

Ramesh and Rahman can do a work in 20 and 25 days respectively. After doing collectively 10 days of work, they leave the work due to illness and Suresh completes rest of the work in 3 days. How many days Suresh alone can take to complete the whole work ? Correct Answer 30 days

(Ramesh & Rahman)'s 1 day's work
$$ = \frac{1}{{20}} + \frac{1}{{25}} = \frac{{5 + 4}}{{100}} = \frac{9}{{100}}$$
∴ Their 10 day's work $$ = \frac{{90}}{{100}} = \frac{9}{{10}}$$
∴ Remaining work $$ = 1 - \frac{9}{{10}} = \frac{1}{{10}}$$
∵ Suresh does $$\frac{1}{{10}}$$ work in 3 days
∴ Time taken by Suresh in doing 1 work = 3 × 10 = 30 days
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