Institution: Bangladesh Bank Exam: Officer (General) -Ansar VDP Unnayan | BD House Building Finance Corporation 28.09.2018 ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To determine how much A will earn if A and B work together on a project that pays Tk. 180, we first need to understand their work rates.

A can complete 1/4 of the work in 3 days, meaning A needs 12 days to finish the entire job (since \( 3 \text{ days} \times 4 = 12 \text{ days} \)). Therefore, A’s work rate is \( \frac{1}{12} \) of the work per day.

B can complete 1/6 of the work in 4 days, which means B also needs 24 days for the whole job (since \( 4 \text{ days} \times 6 = 24 \text{ days} \)). Thus, B’s work rate is \( \frac{1}{24} \) of the work per day.

When A and B work together, their combined work rate is:

\[
\frac{1}{12} + \frac{1}{24} = \frac{2}{24} + \frac{1}{24} = \frac{3}{24} = \frac{1}{8}
\]

This means that A and B together complete \( \frac{1}{8} \) of the work in one day, implying they can finish the entire work in 8 days.

Now, we determine the contribution of A and B to the total work. In 8 days, A will complete:

\[
8 \text{ days} \times \frac{1}{12} = \frac{2}{3} \text{ of the work}
\]

Thus, A does \( \frac{2}{3} \) of the work and B does \( \frac{1}{3} \). The total payment (Tk. 180) is distributed according to the amount of work done, hence:

- A's share: \( \frac{2}{3} \times 180 = 120 \)
- B's share: \( \frac{1}{3} \times 180 = 60 \)

Thus, A will earn Tk. 120, which confirms that the correct answer is **B) Tk. 120**.