A and B can do a work in 10 days and 15 days, respectively. They worked together for 5 days, then B left the work, and A alone did the remaining work. The whole work got completed in:

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Accepted Answer

#### Step 1: Work Done by A and B Together in 1 Day
- Work done by A in 1 day = $$ \frac{1}{10} $$  
- Work done by B in 1 day = $$ \frac{1}{15} $$

Combined work done by A and B in 1 day:  
$$
	ext{Work Together} = \frac{1}{10} + \frac{1}{15} = \frac{3}{30} + \frac{2}{30} = \frac{5}{30} = \frac{1}{6}.
$$

#### Step 2: Work Done by A and B Together in 5 Days
In 5 days, they complete:  
$$
	ext{Work in 5 Days} = \frac{1}{6} 	imes 5 = \frac{5}{6}.
$$

#### Step 3: Remaining Work
The total work is **1 unit**, so the remaining work after 5 days is:  
$$
	ext{Remaining Work} = 1 - \frac{5}{6} = \frac{1}{6}.
$$

#### Step 4: Time Taken by A Alone to Complete Remaining Work
A completes $$ \frac{1}{10} $$ of the work in 1 day. Time taken by A to complete the remaining $$ \frac{1}{6} $$ of the work is:  
$$
	ext{Time by A Alone} = \frac{	ext{Remaining Work}}{	ext{Work by A in 1 Day}} = \frac{\frac{1}{6}}{\frac{1}{10}} = \frac{10}{6} = 1 \frac{2}{3} \, 	ext{days}.
$$

#### Step 5: Total Time to Complete the Work
Total time taken to complete the work is:  
$$
	ext{Total Time} = 	ext{Time Together (5 Days)} + 	ext{Time by A Alone (1 } \frac{	ext{2}}{	ext{3}} 	ext{ Days)}.
$$  
$$
	ext{Total Time} = 5 + 1 \frac{2}{3} = 6 \frac{2}{3}.
$$

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Thus, the whole work got completed in **6 $$\frac{2}{3}$$ days**, making Option **(a)** correct.

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