**Answer:** Option **
A **

**Explanation:**

Given, 3 men and 4 boys together earn Rs. 264 in 8 days and 2 men and 3 boys together earn Rs. 184 in the same time

Now, according to the Chain Rule formula,

M

_{1}D

_{1}W

_{2} = M

_{2}D

_{2}W

_{1}
where, M = No. of person, D = No. of days, W = Amount of work

⇒ (3M + 4B) × 8 × 184 = (2M+ 3B) × 8 × 264

⇒ 3M = 7B ...(i)

Let the no. of days 6 men and 7 boys will work together to earn Rs. 315 be x

(6M + 7B) × x × 184 = (2M + 3B) × 8 × 315

Substituting the relation between men and boys from equation (i) in above equation,

⇒ (14B + 7B) × x × 184 = |
( |
14 |
B + 3B |
) |
× 8 × 315 |

3 |

⇒ 21B × x × 184 = 23B × 8 × 105

⇒ x = 5

Thus, the no. of days 6 men and 7 boys will work together to earn Rs. 315 is 5.