Institution: Bangladesh Bank Exam: Officer (General) |-Sonali | Janata | Bangladesh Krishi_Bangladesh Development bank ২৪.০৫.২০১৯ ||
Topic: Arithmetic Mathematics (পাটিগণিত), Subject: Mathematics (সাধারণ গণিত)

Best Answer Explained in Below-:

To solve the problem, we first need to determine the work rates of both X and Y.

1. **Work Rate of X**: X can complete the entire work in 20 days. Hence, X's work rate is:
\[
\text{Work Rate of X} = \frac{1 \text{ work unit}}{20 \text{ days}} = \frac{1}{20} \text{ work units per day}
\]

2. **Work Rate of Y**: Y can complete \( \frac{1}{7} \) of the work in 5 days. Therefore, Y can complete the total work in:
\[
\text{Total work by Y in 5 days} = \frac{1}{7} \Rightarrow \text{Total work} = 5 \times 7 = 35 \text{ days}
\]
Thus, Y's work rate is:
\[
\text{Work Rate of Y} = \frac{1 \text{ work unit}}{35 \text{ days}} = \frac{1}{35} \text{ work units per day}
\]

3. **Combined Work Rate**: To find their combined work rate, we sum their individual rates:
\[
\text{Combined Rate} = \frac{1}{20} + \frac{1}{35}
\]
To add these fractions, we find a common denominator, which is 140:
\[
\text{Combined Rate} = \frac{7}{140} + \frac{4}{140} = \frac{11}{140} \text{ work units per day}
\]

4. **Time to Complete \( \frac{11}{14} \) of the Work**: We want to find out how long it takes to complete \( \frac{11}{14} \) of the work:
\[
\text{Time} = \frac{\text{Work}}{\text{Rate}} = \frac{\frac{11}{14}}{\frac{11}{140}} = \frac{11}{14} \times \frac{140}{11} = 10 \text{ days}
\]

Therefore, X and Y together can complete \( \frac{11}{14} \) of the total work in **10 days**, making the correct answer option C.