Institution: Bangladesh Bank Exam: অফিসার (ক্যাশ ) - Sonali | Rupali | BD Krishi | Rajshahi Krishi Unnayn | Investment Corporation Of Bangladesh - ২৯. ০৩.২০১৯ ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem of finding the ratio of the first number (let's call it \( x \)) to the second number (let's call it \( y \)), we start with the information provided: 40% of \( x \) is equal to two-thirds of \( y \). This can be expressed mathematically as:

\[ 0.4x = \frac{2}{3}y \]

To eliminate the decimals and fractions, we can multiply both sides of the equation by 30 (the least common multiple of the denominators):

\[ 30 \times 0.4x = 30 \times \frac{2}{3}y \]

This simplifies to:

\[ 12x = 20y \]

Next, we want to find the ratio \( x:y \). We can rearrange the equation:

\[ \frac{x}{y} = \frac{20}{12} \]

By simplifying \( \frac{20}{12} \), we divide both the numerator and the denominator by their greatest common divisor, which is 4:

\[ \frac{x}{y} = \frac{5}{3} \]

This means the ratio of the first number \( x \) to the second number \( y \) is \( 5:3 \). Thus, the correct answer is option B, \( 5:3 \). Through the calculations, we see how the proportional relationship between the two numbers emerges clearly, leading to this final ratio.