If A : B = 5 : 2, B : C = 2 : 3 and C: D = 5: 3 , ` then the ratio A: B : C : D is

Options

A. ` 25 : 10 : 15 :9`
B. ` 10 : 5 : 3 : 2`
C. ` 15 : 5 : 3 : 2`
D. ` 25 : 10 : 15 : 3`

Answer

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

### Step 1: Write down the given ratios
We have:
- A : B = 5 : 2
- B : C = 2 : 3
- C : D = 5 : 3

### Step 2: Express the ratios in fractional form
From the ratios, we can express them as:
- A/B = 5/2
- B/C = 2/3
- C/D = 5/3

### Step 3: Find a common term for B and C
To combine these ratios, we need to make sure that the value of B and C is the same in both ratios. The value of B in the first ratio is 2, and in the second ratio, it is also 2. Therefore, we can directly use these ratios.

### Step 4: Equalize the value of C
Now, we need to make the value of C the same in both B : C and C : D.
From B : C = 2 : 3, we can express C in terms of B:
- C = (3/2)B

From C : D = 5 : 3, we can express D in terms of C:
- D = (3/5)C

### Step 5: Substitute C in terms of B into C : D
Now we substitute C from the first equation into the second:
- D = (3/5)(3/2)B = (9/10)B

### Step 6: Now we have all terms in terms of B
Now we can express A, B, C, and D in terms of B:
- A = 5/2 B
- B = B
- C = (3/2)B
- D = (9/10)B

### Step 7: Convert all terms to a common denominator
To express the ratios in whole numbers, we can multiply each term by 10 (the least common multiple of the denominators):
- A = (5/2) * 10 = 25
- B = 10
- C = (3/2) * 10 = 15
- D = (9/10) * 10 = 9

### Step 8: Write the final ratio
Now we can write the combined ratio:
A : B : C : D = 25 : 10 : 15 : 9

### Final Answer
The ratio A : B : C : D is 25 : 10 : 15 : 9.

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