Question

a can fo a piece of work in 10 days and b in 20 days. they begin together but a leaves 2 days before the completion of the work. in how many days will the whole work be completed​

Answer 1

Given:-

• A can do a piece of work in 10days.
• B can do it in 20 days.
• They begin together but A leaves 2 days before the completion of the work.

To find:-

• No.of.days in which the whole work will be completed.

Solution:-

Let us consider that the work is done in 'x' days

Then,

In 1 day:

Work of A = 1/10

Work of B = 1/20

Given that A leaves 2 days before,

A works for (x-2) &

B works for x days

According to question,

$\displaystyle :\implies \sf \frac{x-2}{10} +\frac{x}{20} =1\\\\\\:\implies \sf 2(x-2)+x = 20\\\\\\:\implies \sf 2x-4+x = 20\\\\\\:\implies \sf 3x = 20+4\\\\\\:\implies \sf x = \frac{24}{3} \\\\\\:\implies \underline{\boxed{\bold{x=8.}}}$

Hence,

The work will be completed in 8 days.

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