If 6 BSF or 10 CRPF companies can demolish a terrorist outfit in Kashmir in 2 days, find how long will 4 BSF and 9 CRPF companies take to do the same ?

Options

A. 1.27 days
B. 2.27 days
C. 3.27 days
D. 4.27 days

Answer

To solve the problem, we need to determine how long it will take for 4 BSF and 9 CRPF companies to demolish the terrorist outfit, given that 6 BSF or 10 CRPF companies can do the same in 2 days.

### Step-by-Step Solution:

1. **Determine the Work Done by Each Group**:
- If 6 BSF companies can complete the work in 2 days, then the total work can be expressed in terms of BSF companies:
\[ \text{Work} = \text{Number of Companies} \times \text{Time} = 6 \text{ BSF} \times 2 \text{ days} = 12 \text{ company-days} \]
- Similarly, if 10 CRPF companies can complete the work in 2 days:
\[ \text{Work} = 10 \text{ CRPF} \times 2 \text{ days} = 20 \text{ company-days} \]

2. **Calculate the Work Rate**:
- From the above calculations, we can see that the total work done is the same, so we can equate the two:
\[ 12 \text{ company-days} = 20 \text{ company-days} \]
- This means that the work done by each BSF company is equivalent to the work done by \(\frac{20}{12} = \frac{5}{3}\) CRPF companies.

3. **Convert BSF Companies to CRPF Equivalent**:
- Now, we need to convert the 4 BSF companies into CRPF equivalent:
\[ 4 \text{ BSF} = 4 \times \frac{5}{3} \text{ CRPF} = \frac{20}{3} \text{ CRPF} \]
- Therefore, the total number of CRPF companies equivalent to 4 BSF and 9 CRPF is:
\[ \frac{20}{3} + 9 = \frac{20}{3} + \frac{27}{3} = \frac{47}{3} \text{ CRPF} \]

4. **Calculate the Time Taken by 4 BSF and 9 CRPF**:
- Now we need to find out how long it will take for \(\frac{47}{3}\) CRPF companies to complete the work of 20 company-days:
\[ \text{Time} = \frac{\text{Total Work}}{\text{Total Companies}} = \frac{20 \text{ company-days}}{\frac{47}{3} \text{ CRPF}} = 20 \times \frac{3}{47} = \frac{60}{47} \text{ days} \]

5. **Final Answer**:
- Therefore, the time taken by 4 BSF and 9 CRPF companies to demolish the terrorist outfit is approximately:
\[ \frac{60}{47} \text{ days} \approx 1.28 \text{ days} \]