Question

'A' can do a piece of work in 25 days and 'B' can finish it in 20 days. how many days will they take if they work together.

Answer 1

A can do the piece of work in 25 days

1 day =  1/25 of the work

A can do the piece of work in 20 days

1 day = 1/20 of the work

If the work together:

1 day = 1/25 + 1/20 = 9/100

Number of days needed:

9/100 of the work = 1 day

1/100 of the work = 1 ÷ 9 = 1/9 day

100/100 of the work = 1/9 x 100 = 100/9 = 11.11 days

Answer: They need 11.11 days.

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SHORTCUT:

Number of days needed = (25 x 20) / (25 + 20) = 100/9 = 11.11 days

Answer: They need 11.11 days.

Answer 2

Solutions :-



A' can do a piece of work in 25 days
The work done by 'A' in one day = 1/25


'B' can finish it in 20 days.
The work done by 'B' in one day = 1/20


Find the work done by 'A' and 'B' in one day :-

$\frac{1}{25} + \frac{1}{20} \\ \\ \frac {4 \: \: \: \: + \: \: \: 5}{100} = \frac{9}{100}$



Find the number of days needed :-

= 9/100 of the work = 1 day
= 1 of the work = 1 × 100/9 = 100/9 = 11.11 approx.


Hence,
Both can do a work in 11.11 days or 11 days 2 hours and 38 minutes