Question

two number are in the ratio2:3 if 5 is added to each of them the ratio become 5:7 find the number​

Answer 1

Answer.....

Let the two numbers be 2x and 3x.

According to the given information

$\frac{2x + 5}{3x + 5} = \frac{5}{7}$

14x + 35 = 15x + 25x

x = 10

Thus, the numbers are

2 × 10 = 20

3 × 10 = 30

Answer 2

Step-by-step explanation:

Given: ratio of number =2: 3

after adding 5 to both numbers ratio become =5: 7

To find: The numbers

$\color{red} \underline{ \begin{array}{ || |l| || } \hline \color{magenta} \\ \hline \boxed{ \text{ \tt \: Solution:-} } \end{array}}$

let the numbers are x and y.

$\text{so \( \tt\dfrac{x}{y}=\dfrac{2}{3} \quad \) (given)}$

$\text{ \( \tt3 x=2 y \Rightarrow x=\dfrac{2}{3} y \) \: \: \: \: \: \: \: \: \: \: \: \: - - - - (1)}$

$\text{also \( \tt \dfrac{x+5}{y+5}=\dfrac{5}{7} \) now from 1}$

$\color{darkcyan} \[ \begin{array}{l} \tt \left(\dfrac{2 y}{3}+5\right) \times 7=5 \times(y+5) \\ \\ \tt\dfrac{14 y}{3}+35=5 y+25 \\ \\ \tt\dfrac{14 y}{3}-5 y=25-35 \qquad\Rightarrow \dfrac{14 y-15 y}{3}=-10 \\ \\ \tt -\dfrac{y}{3}=-10 \\ \\ \tt \: y=3030 \\ \\ \tt \: x=30 x \dfrac{2}{3} \\ \\ \tt x=20 \end{array} \]$

Answer: Hence; The numbers are 20 and 30 .