Question

Two numbers are in the ratio $$5 : 7$$. If 8 is subtracted from each, the ratio becomes $$3 : 5$$. Find the numbers.

Answer 1

Let the two numbers be $$5x$$ and $$7x$$. 

According to the question: $$\frac{5x - 8}{7x - 8} = \frac{3}{5}$$ 

Cross-multiply: $$5(5x - 8) = 3(7x - 8)$$

$$25x - 40 = 21x - 24$$ 

Solve for $$x$$: $$25x - 21x = 40 - 24$$

$$4x = 16 \implies x = 4$$ 

The numbers are:

First number = $$5 \times 4 = 20$$

Second number = $$7 \times 4 = 28$$

Therefore, the numbers are 20 and 28.