If 6 girls and 8 boys can complete a project work in 10 days, whereas 26 girls and 48 boys can do the same work in 2 days, then find the time taken by 10 girls and 30 boys to do the same type of work.

Correct option is D

Given:
6 girls and 8 boys complete the work in 10 days.
26 girls and 48 boys complete the same work in 2 days.
We need to find the time taken by 10 girls and 30 boys to complete the same work.
Formula Used:
Work = Time × Total efficiency
Efficiency of a group is the sum of individual efficiencies of its members.
Solution:
Let the efficiency of 1 girl = g and 1 boy = b.
Total work = 10 × (6g + 8b) = 2 × (26g + 48b) 
60g + 80b = 52g + 96b
=> 60g - 52g = 96b - 80b
=> 8g = 16b
=> g = 2b
Now, substitute g = 2b in the total work equation:
Total work = 60g + 80b = 60(2b) + 80b= 120b + 80b = 200b
For 10 girls and 30 boys:
Efficiency = 10g + 30b = 10(2b) + 30bn= 20b + 30b = 50b
Time taken = Total work / Efficiency
=> Time = $$\frac{200b}{50b}$$​ = 4 days