Let’s solve the question shown in the image.

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Given:

A can complete the job in 21 days → A’s 1 day work =

B can complete the job in 14 days → B’s 1 day work =

A works alone for 6 days.

Then A and B work together to complete the job.

We need to find how many days the work lasted in total.

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Step 1: Work done by A in 6 days

A’s 1 day work =

In 6 days, A does:

6 \times \frac{1}{21} = \frac{6}{21} = \frac{2}{7}

So, work remaining =

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Step 2: A and B working together

A’s 1 day work =

B’s 1 day work =

Together in 1 day they do:

\frac{1}{21} + \frac{1}{14} = \frac{2 + 3}{42} = \frac{5}{42}

Let the number of days A and B worked together be

Then,

x \times \frac{5}{42} = \frac{5}{7}

Solve for :

x = \frac{5}{7} \div \frac{5}{42} = \frac{5}{7} \times \frac{42}{5} = 6

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Step 3: Total duration of work

A worked 6 days alone

Then A and B worked together for 6 more days

Total = 6 + 6 = 12 days

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✅ Final Answer: 12 days

But note: this is not listed as an option. Options given are:

A) 5

B) 8

C) 7

D) 6

Looks like the question is asking “How many days did the work last in total?”, which is 12, but perhaps it meant:

How many more days did they work together after the first 6 days?

In that case, the number of days A and B worked together is 6, so:

✅ Correct Option: D) 6