There were some red, black and blue pens in a drawer. 1/3 of the pens were red and the number of black pens was 11 less than 1/2 of the number of red pens. If there were 284 blue pens, how many black pens were there in the drawer?
given data in
1/3rd of the pens are red.
number of black pens was 11 pens then 1/2 of the red pens.
There were total 284 blue pens.
To find number of black pens.
Assume that there are x red pen, y black pens, z blue pens, then
x = 1/3 (x + y + z)
z = 284 and y+11=1/2x
=> 3x = x + y + z ; z = 284 ; 2y+22=x
4y + 44 - y = 284
3y = 240
y = 80 x = 2 (80) + 22 = q82
x = 182
Thus there were total 80 black pens.