If `A:B=3:4, B:C=5:2` then find the value of A:B:C.

Answer

To find the value of A:B:C given the ratios A:B = 3:4 and B:C = 5:2, we can follow these steps:

### Step 1: Write the given ratios in fractional form
From the problem, we have:
- A:B = 3:4, which can be written as \( \frac{A}{B} = \frac{3}{4} \)
- B:C = 5:2, which can be written as \( \frac{B}{C} = \frac{5}{2} \)

### Step 2: Express A and C in terms of B
From the first ratio \( \frac{A}{B} = \frac{3}{4} \), we can express A in terms of B:
\[ A = \frac{3}{4}B \]

From the second ratio \( \frac{B}{C} = \frac{5}{2} \), we can express C in terms of B:
\[ C = \frac{2}{5}B \]

### Step 3: Find a common value for B
To combine these ratios, we need to find a common value for B. The easiest way is to express B in terms of a common multiple. The denominators of the fractions for A and C are 4 and 5, respectively. The least common multiple (LCM) of 4 and 5 is 20.

Let's set B = 20.

### Step 4: Calculate A and C using B = 20
Now we can find the values of A and C:
- For A:
\[ A = \frac{3}{4} \times 20 = 15 \]

- For C:
\[ C = \frac{2}{5} \times 20 = 8 \]

### Step 5: Write the final ratio A:B:C
Now we have:
- A = 15
- B = 20
- C = 8

Thus, the ratio A:B:C is:
\[ A:B:C = 15:20:8 \]

### Final Answer:
The value of A:B:C is \( 15:20:8 \).

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