The no. of Red, Yellow and Purple marbles are 72, 108, 216 respectively.
<u>Step-by-step explanation:</u>
Let us consider the no. of red marbles be R
Let the no. of yellow marbles be Y
Let the no. of purple marbles be P
Given that there are 396 marbles in the bag.
Total marbles = R+ Y + P
396 = R + Y + P
The ratios are given as below:
R : Y =2/3
Which means, R/Y = 2/3
R= 2Y/3
Y: P = 1/2
Which means, Y/P = 1/2
1/P = 1/2Y
P = 2Y
Here we got the values of P and R in terms of Y.
Total marbles = R + Y + P
396 =( 2Y/3) +Y+(2Y)
Taking LCM, we have 3 as LCM
396 = (2Y +3Y+ 6Y) / 3
396 x 3 = 2Y + 3Y + 6Y
1188 = 11Y
11Y = 1188
Y = 1188/11
Y = 108
R/Y = 2/3
R/108 = 2/3
R = 2(108) /3
R= 72
Y/P = 1/2
108/ P = 1/2
1/P = 1/2(108)
P = 2(108)
P = 216
The no. of Red, Yellow and Purple marbles are 72, 108, 216 respectively.
