Question

A and B start a work and finish half of it in 10 days.the rest is done by B in 100 days.in how many days can A alone do the entire work?

Answer 1

Answer:

10days

Step-by-step explanation:

100/10=10days .

Answer 2

A alone can do the entire work in $\frac{200}{9}\ or\ 22\frac{2}{9}\ days$

Solution:

Given that,

A and B start to work together and finish half of the work in 10 days

Which means within 20 days both should have completed the full work

One day work A & B together = $\frac{1}{20}$

B took 100 days for completing half work

So B alone will complete entire work in 200 days

So one day work of B = $\frac{1}{200}$

One day work of A = One day work of A & B - one day work of B

Therefore,

$\frac{1}{A} = \frac{1}{20} - \frac{1}{200}\\\\\frac{1}{A} = \frac{1 \times 10}{20 \times 10} - \frac{1}{200}\\\\\frac{1}{A} = \frac{10}{200} - \frac{1}{200}\\\\\frac{1}{A} = \frac{10-1}{200}\\\\\frac{1}{A} = \frac{9}{200}$

Thus, A alone can do the entire work in:

$A = \frac{200}{9} = 22\frac{2}{9}$

Thus A alone can do the entire work in $\frac{200}{9}\ or\ 22\frac{2}{9}\ days$

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