If A/B=2/3 and B/C=1/3 , then find the value of A: B: C is_______ .

Correct option is C

Solution:

​Step 1: Express A in terms of B from the first ratio
From A/B = 2/3, we get:
A = (2/3) * B

Step 2: Express B in terms of C from the second ratio
From B/C = 1/3, we get:
B = (1/3) * C

Step 3: Substitute the value of B in terms of C into the expression for A
Substitute B = (1/3) * C into A = (2/3) * B:
A = (2/3) * (1/3) * C = (2/9) * C

Step 4: Now, express A : B : C
We now have:
A = (2/9) * C
B = (1/3) * C
C = C

So, A : B : C = (2/9) * C : (1/3) * C : C

Step 5: Simplify the ratio
We can cancel out C from all terms, and we get:
A : B : C = 2/9 : 1/3 : 1

To simplify, multiply all terms by 9 (the LCM of 9, 3, and 1):
A : B : C = (2/9) * 9 : (1/3) * 9 : 1 * 9
A : B : C = 2 : 3 : 9

Final Answer:
A : B : C = 2 : 3 : 9