Establish Work Equality

Total work is $(18B + 24G) \times 16$. Work done in 12 days is $(18B + 24G) \times 12$. Remaining work is $(18B + 24G) \times (16 - 12) = (18B + 24G) \times 4$.

$(18B + 24G) \times 4 = 12B \times 9$

Determine Ratio of Efficiency

Simplify the equation: $72B + 96G = 108B$, which gives $96G = 36B$. Dividing by 12, $8G = 3B$.

$B = \frac{8}{3}G$

Calculate Total Work

Substitute $B = \frac{8}{3}G$ into the total work expression: $W = (18(\frac{8}{3}G) + 24G) \times 16 = (48G + 24G) \times 16 = 72G \times 16$.

$W = 1152G$

Find Time for 24 Girls

Time taken by 24 girls is $T = \frac{\text{Total} \text{Work}}{\text{Efficiency}} = \frac{72G \times 16}{24G} = 3 \times 16 = 48$.

$T = 48 \text{ days}$