Ten boys and twelve girls collected for donations for a project. The amount collected by the boys was #600:00 greater than that collected by the girls. If the average collection of boys was #100:00 greater than the average collection of the girls, how much was collected by the two groups

Dear student,
The currency is not clearly mentioned in the question. I am assuming it as rupees.
Let x rs represent the donation collected by the girls.
Then, the donation collected by the boys = (x + 600) rs

Also, let y rs represent the average collection of the girls.
Then the average collection of the boys = (y + 100) rs

Thus, x/12=y

x=12y...(1)

also
(x+600)/10=y+100
x+600=10(y+100)....(2)

Substitute 12y for x in (2) :

12y+600=10y+1000
or, 12y−10y=1000−600
or, 2y=400
or, y=200 

From (1), x=12y

∴x=12×200=2,400 

Thus, the girls collected 2,400 rs

The boys collected 2,400 + 600 = 3000 rs

Total = (2,400 + 3,000) = 5,400 rs

Regards