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,
M₁D₁W₂ = M₂D₂W₁
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 = (14/3B + 3B) x 8 x 315
⇒  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.