Question

On adding 10 to each of the number of ratio in 3 : 5, the ratio becomes 5 : 7, the numbers are…………

Answer 1

$\bf{\large{\underline{\underline{Solution:}}}}$

Let the numbers be 3x and 5x

[Adding 10 to both the sides]

Then, A/Q

5(5x+10) = 7(3x+10)

25x+50 = 21x+70

25x-21x = 70-50

4x = 20

x = 20/4

x = 5

Hence, the numbers are:

3x = 3 × 5 = 15

5x = 5 × 5 = 25

Answer 2

$\large{\mathfrak{\underline{\underline{Solution:-}}}}$

_____________________

Let the numbers be 3x and 5x (according to their given ratio i.e, 3:5)

Therefore, ATQ

$\large{\boxed{\frac{3x + 10}{5x + 10} = \frac{5}{7} }}$ (Equation formed)

$\large{⇒ 7(3x + 10) = 5(5x + 10) }$

$\large{⇒ 21x + 70 = 25x + 50}$

$\large{⇒ 21x - 25x = 50 - 70 }$

$\large{⇒ - 4x = - 20 }$

$\large{⇒ x = \frac{-20}{-4} }$

$\boxed{\red{ x = 5}}$

Thus, the numbers are

$\large{3x = 3 \times 5 = 15}$

$\large{5x = 5 \times 5 = 25}$