The cost of an apple is twice that of a banana and the cost of a banana is \(25\%\) less than that of a guava. If the cost of each type of fruit increases by \(10\%\), then the percentage increase in the cost of \(4\) bananas, \(2\) apples and \(3\) guavas is: একটি আপেলের দাম একটি কলার দামের দ্বিগুণ এবং একটি কলার দাম একটি পেয়ারার দামের থেকে \(25\%\) কম। যদি প্রতিটি ফলের দাম \(10\%\) বৃদ্ধি পায়, তবে \(4\) টি কলা, \(2\) টি আপেল এবং \(3\) টি পেয়ারার মোট দামের শতকরা বৃদ্ধি কত হবে?

Let the cost of a guava be \(100\).

Since the cost of a banana is \(25\%\) less than that of a guava:

\[ \text{Cost of banana} = 100 - 25 = 75 \]

The cost of an apple is twice that of a banana:

\[ \text{Cost of apple} = 2 \times 75 = 150 \]

Initial total cost of \(4\) bananas, \(2\) apples and \(3\) guavas:

\[ 4 \times 75 + 2 \times 150 + 3 \times 100 \]

\[ = 300 + 300 + 300 = 900 \]

Since the cost of each fruit increases by \(10\%\), the total cost will also increase by \(10\%\).

New total cost:

\[ 900 + 10\% \times 900 \]

\[ = 900 + 90 = 990 \]

Percentage increase:

\[ \frac{990 - 900}{900} \times 100 = 10\% \]

Correct Option: A