If 15% of A is equal to 20% of B and 10% of B is equal to 25% of C, what is the ratio of A : B : C?

The correct option is 20:15:6.

To find the ratio A : B : C, let us break down the given relationships step-by-step.

Step 1: Express the relationship between A and B
We are given that 15% of A is equal to 20% of B.
Mathematically, this can be written as:

$$15\%\times A=20\%\times B$$

Converting percentages to fractions:

$$\frac{15}{100}A=\frac{20}{100}B$$

Multiplying both sides by 100 simplifies this to:

$$15A=20B$$

Dividing both sides by 5:

$$3A=4B$$

Thus, the ratio of A to B is:

$$\frac{A}{B}=\frac{4}{3}$$

This means A : B = 4 : 3.

Step 2: Express the relationship between B and C
We are given that 10% of B is equal to 25% of C.
Mathematically, this can be written as:

$$10\%\times B=25\%\times C$$

Converting percentages to fractions:

$$\frac{10}{100}B=\frac{25}{100}C$$

Multiplying both sides by 100 simplifies this to:

$$10B=25C$$

Dividing both sides by 5:

$$2B=5C$$

Thus, the ratio of B to C is:

$$\frac{B}{C}=\frac{5}{2}$$

This means B : C = 5 : 2.

Step 3: Combine the ratios to find A : B : C
We have:
A : B = 4 : 3
B : C = 5 : 2

To combine these ratios, we need the value representing B to be the same in both ratios. The lowest common multiple (LCM) of the B values (3 and 5) is 15.

Multiply the terms of A : B by 5:

$$A:B=(4\times 5):(3\times 5)=20:15$$

Multiply the terms of B : C by 3:

$$B:C=(5\times 3):(2\times 3)=15:6$$

Now that the value of B is unified as 15 in both ratios, we can combine them directly:
A : B : C = 20 : 15 : 6