Step 1: Set up the work equation

Since total work remains constant, the product of workers and days in both cases is equal: $(6M + 8B) \times 10 = (26M + 48B) \times 2$

$60M + 80B = 52M + 96B$

Step 2: Find the efficiency ratio of Men to Boys

Simplify the equation to find the relation between a man ($M$) and a boy ($B$): $60M - 52M = 96B - 80B \implies 8M = 16B \implies M = 2B$

$1 \text{ man} = 2 \text{ boys}$

Step 3: Calculate Total Work in units

Substitute $M = 2B$ into the first case expression: $\text{Total Work} = (6(2B) + 8B) \times 10 = (12B + 8B) \times 10 = 20B \times 10 = 200 \text{ units}$

$\text{Total Work} = 200 \text{ units}$

Step 4: Find efficiency of the target group and calculate time

The target group consists of 10 men and 20 boys: $\text{Efficiency} = 10(2B) + 20B = 20B + 20B = 40B\text{Time} = \frac{200}{40} = 5 \text{ days}$

$5 \text{ days}$