Institution: CITY BANK LTD Exam: City Bank Ltd - Probationary Officer - 02.12.2011 ||
Topic: Mathematics (সাধারণ গণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To understand why the value of the fraction \( \frac{XZ}{Y} \) remains the same when both \( X \) and \( Y \) are tripled, let’s break down the fraction mathematically.

Initially, we have the fraction \( \frac{XZ}{Y} \). Now, if \( X \) and \( Y \) are both tripled, we can express this as follows:

- \( X \) becomes \( 3X \)
- \( Y \) becomes \( 3Y \)

Substituting these new values into the fraction gives us:

\[
\frac{(3X)Z}{3Y}
\]

We can simplify this new fraction:

\[
= \frac{3XZ}{3Y}
= \frac{XZ}{Y}
\]

When we divide by the same number in the numerator and denominator (in this case, the 3's), the overall value of the fraction does not change. Therefore, the fraction \( \frac{XZ}{Y} \) before and after tripling \( X \) and \( Y \) remains exactly the same.

In conclusion, even though \( X \) and \( Y \) were adjusted, they both influence the fraction proportionally, leaving its value unchanged. Thus, the correct answer is D) remains the same.