Question

Two numbers are such that the ratio between them is 3 : 5. If each is increased by 10, the ratio between the new numbers so formed is 5 : 7. Find the original numbers.

Answer 1

Ratio between two numbers = 3 : 5

Let first number = 3x

and second number = 5x

Now According to the condition,

3x + 10 : 5x + 10 = 5 : 7

$\Rightarrow \frac{3x+10}{5x+10}=\frac{5}{7}$

$\Rightarrow$ 7 (3x + 10) = 5 (5x + 10)

(By cross multiplication)

21x + 70 = 25x + 50

$\Rightarrow$ 21x - 25x = 50 - 70 $\Rightarrow$ -4x = - 20

$\Rightarrow$ 4x = 20 $\Rightarrow x=\frac{20}{4}=5$

$\therefore$ first number = 3x = 3 $\times$ 5 = 15

and second number 5x = 5 $\times$ 5 = 25

Hence numbers are 15, 25 Ans.