Question

9. A can do a piece of work in 10 days and B in 20 days. They begin together but A leaves 2 days before th
completion of the work. In how many days will the whole work be completed?
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Answer 1

Let the required days be x.

A works for (x - 2) days, while B works for x days.

According to the question.

x−210+x20=1

2x- 4 + x = 20

3x = 24

x = 8 days

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Answer 2

Given :

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

To find :

• In how many days will the whole work be completed ?

Solution :

• Work done by A in 1 day = 100/10 % = 10%

• Work done by B in 1 day = 100/20 % = 5%

Now,

Total work done by both A and B together = 15%.

Let the number of days to complete work be x.

Here,

• A leaves work before 2 days of completion.

Therefore, A and B worked together for (x-2) days.

• B worked for 2 days.

→ 15% × x(x-2) + 5% × 2 = 100%

→ 15/100 % × (x-2) + 5/100 × 2 = 100/100

→ 3/20 × (x-2) + 1/20 × 2 = 1

→ 3/20 × -3/10 + 1/10 = 1

→ 3x - 4 = 20

→ 3x = 20 + 4

→ 3x = 24

→ x = 24/3

→ x = 8

Therefore, It will take 8 days for the total work to be done.