Question

If $$3\mathrm{A} = 5\mathrm{B} = 6\mathrm{C}$$, find $$\mathrm{A}:\mathrm{B}:\mathrm{C}$$.

Answer 1

Let $$3\mathrm{A} = 5\mathrm{B} = 6\mathrm{C} = k$$.

Then, $$\mathrm{A} = \frac{k}{3}$$, $$\mathrm{B} = \frac{k}{5}$$ and $$\mathrm{C} = \frac{k}{6}$$.

$$\mathrm{A} : \mathrm{B} : \mathrm{C} = \frac{1}{3} : \frac{1}{5} : \frac{1}{6}$$.

The L.C.M. of the denominators 3, 5 and 6 is 30. 

Multiply each term by 30:

$$\mathrm{A} = \frac{1}{3} \times 30 = 10$$

$$\mathrm{B} = \frac{1}{5} \times 30 = 6$$

$$\mathrm{C} = \frac{1}{6} \times 30 = 5$$

Therefore, $$\mathrm{A} : \mathrm{B} : \mathrm{C} = 10 : 6 : 5$$.