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15 Jul 2026, 05:01
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Here's my solution for this question
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15 Jul 2026, 05:05
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The correct selections is 72 beads for container 1 and 64 beads for container 2.
In container 1, the ratio is 1:3:2
Total parts: 1+3+2= 6 parts
Gold beads(G1)= 1/6 T1
Green beads (Gr1)= 3/6T1= 1/2 T1
Container 2, the ratio is 4:1:3
Total parts: 4+1+3= 8 parts
Gold beads (G2)= 4/8T2=1/2 T2
Green Beads (Gr2)= 1/8 T2
G1+G2= Gr1+Gr2
1/6T1+ 1/2 T2= 1/2 T1+1/8T2
1/2T2- 1/8 T2= 1/2 T1-1/6T1
3/8 T2= 1/3 T1
9T2= 8T1
T1/T2=9/8
Now lets compare the given answer choices.
For every 9 units in Container 1, there must be 8 units in container 2.
1. Lets consider T1=40
T2= T1*8/9= not an integer value, hence this is not the answer.
2. Lets consider T1= 45
T2= 45*8/9= 40
This cannot be the answer because the green and the gold beads will than be in non integer form.
Let's check for 72, in container 1
T2= 72*8/9
T2= 64
This is our answer because both the beads are in integer forms as well.
In container 1, the ratio is 1:3:2
Total parts: 1+3+2= 6 parts
Gold beads(G1)= 1/6 T1
Green beads (Gr1)= 3/6T1= 1/2 T1
Container 2, the ratio is 4:1:3
Total parts: 4+1+3= 8 parts
Gold beads (G2)= 4/8T2=1/2 T2
Green Beads (Gr2)= 1/8 T2
G1+G2= Gr1+Gr2
1/6T1+ 1/2 T2= 1/2 T1+1/8T2
1/2T2- 1/8 T2= 1/2 T1-1/6T1
3/8 T2= 1/3 T1
9T2= 8T1
T1/T2=9/8
Now lets compare the given answer choices.
For every 9 units in Container 1, there must be 8 units in container 2.
1. Lets consider T1=40
T2= T1*8/9= not an integer value, hence this is not the answer.
2. Lets consider T1= 45
T2= 45*8/9= 40
This cannot be the answer because the green and the gold beads will than be in non integer form.
Let's check for 72, in container 1
T2= 72*8/9
T2= 64
This is our answer because both the beads are in integer forms as well.
15 Jul 2026, 06:07
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Total beads in the Container 1 is given as - Gold : Green : White = 1:3:2 = 1n+3n+2n = 6n
Total beads in the Container 2 is given as - Gold: Green : White = 4:1:3 = 4y+1y+3y = 8y
Also 1n+ 4y = 3n+1y => 3y = 2n
Now, using the above equations, I will use trial and error method as below:
Option a - 40 - Container 1 - False since not divisible by 6, It is divisible by 8 - But since not by 6, I have eliminated
Option b - 45 - Container 1 - False since not divisible by 6 or 8
Option c - 54 - Container 1 - possible but container 2 not possible
Option d - 64 - Container 1 not possible but Container 2 possible
Option e - 72 - Divisible by both 6 and 8
Option f - 81 - Container 1 - not possible since not divisible by 6
So 2 options => 54 and 72
When we use 72 in Container 1 - green beads = 36 = 3n, 2n = 24 = 3y => y=8
Container 2 = 8*8 = 64
Hence by above we get the answer as Container 1 - 72 and Container 2 - 64
Total beads in the Container 2 is given as - Gold: Green : White = 4:1:3 = 4y+1y+3y = 8y
Also 1n+ 4y = 3n+1y => 3y = 2n
Now, using the above equations, I will use trial and error method as below:
Option a - 40 - Container 1 - False since not divisible by 6, It is divisible by 8 - But since not by 6, I have eliminated
Option b - 45 - Container 1 - False since not divisible by 6 or 8
Option c - 54 - Container 1 - possible but container 2 not possible
Option d - 64 - Container 1 not possible but Container 2 possible
Option e - 72 - Divisible by both 6 and 8
Option f - 81 - Container 1 - not possible since not divisible by 6
So 2 options => 54 and 72
When we use 72 in Container 1 - green beads = 36 = 3n, 2n = 24 = 3y => y=8
Container 2 = 8*8 = 64
Hence by above we get the answer as Container 1 - 72 and Container 2 - 64
15 Jul 2026, 06:08
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Let the total number beads in Container 1 and 2 be X and Y respectively.
Container 1:
Gold: Total = 1:6
So Gold = X/6.
Green:Total = 3/6
Green = Total/2=X/2
For Container 2:
Gold : Y = 4:8
Gold = Y/2
Green: Y = 1:8
Green = Y/8
Also given that:
X/6 + X/2 = Y/2 + Y/6
Solving we get 8X = 9Y
We need to align with options where X = 6k and Y = 8m
Options divisible by 6 are: 54 and 72
Options divisible by 8 are: 40, 64, 72
Plugging in we get only one way of possibility 8 (72) = 9 (64) = 576
So container 1: 72
Container 2: 64 are the ans IMO
Container 1:
Gold: Total = 1:6
So Gold = X/6.
Green:Total = 3/6
Green = Total/2=X/2
For Container 2:
Gold : Y = 4:8
Gold = Y/2
Green: Y = 1:8
Green = Y/8
Also given that:
X/6 + X/2 = Y/2 + Y/6
Solving we get 8X = 9Y
We need to align with options where X = 6k and Y = 8m
Options divisible by 6 are: 54 and 72
Options divisible by 8 are: 40, 64, 72
Plugging in we get only one way of possibility 8 (72) = 9 (64) = 576
So container 1: 72
Container 2: 64 are the ans IMO
Bunuel
