Institution: SONALI BANK LTD Exam: Sonali Bank Ltd - Assistant Engineer (IT) - 26.08.2016 ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To find out how long Sam and Mark will take to mow the lawn together, we first need to determine their individual rates of work.

Sam can mow the lawn in 20 minutes, which gives him a rate of:
\[ \text{Rate of Sam} = \frac{1 \text{ lawn}}{20 \text{ min}} = 0.05 \text{ lawns/min} \]

Mark takes 10 minutes longer than Sam, so he can mow the lawn in:
\[ 20 \text{ min} + 10 \text{ min} = 30 \text{ min} \]
His rate is:
\[ \text{Rate of Mark} = \frac{1 \text{ lawn}}{30 \text{ min}} = \frac{1}{30} \text{ lawns/min} \]

When they work together, their rates add up:
\[ \text{Combined Rate} = 0.05 + \frac{1}{30} \]

To add these rates, convert 0.05 to a fraction:
\[ 0.05 = \frac{1}{20} \]
Now we need a common denominator to add \(\frac{1}{20}\) and \(\frac{1}{30}\). The least common multiple of 20 and 30 is 60.

Converting the fractions:
\[ \frac{1}{20} = \frac{3}{60} \]
\[ \frac{1}{30} = \frac{2}{60} \]

Now, add the rates:
\[ \text{Combined Rate} = \frac{3}{60} + \frac{2}{60} = \frac{5}{60} = \frac{1}{12} \text{ lawns/min} \]

To determine the time taken to mow one lawn together, we take the reciprocal of their combined rate:
\[ \text{Time} = \frac{1 \text{ lawn}}{\frac{1}{12} \text{ lawns/min}} = 12 \text{ min} \]

Thus, working together, Sam and Mark will take 12 minutes to mow the lawn, which corresponds to option A.