Question

Q. Two numbers are in the ratio 2:5. When 7 is added to each of them, the ratio is changed to 9: 19. Find the numbers
$step \: by \: step \: answer$
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Answer 1

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

The two numbers are 20 and 50.

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

Given :

The ratio of the Numbers = 2 : 5

The new ratio when 7 is added to them = 9 : 19

To Find :

The Numbers

Solution :

◆ $\textbf{\small{\underline{Consider the Original Numbers as -}}}$

• 2x
• 5x

$\rule{300}{1.5}$

◆ $\textbf{\small{\underline{According to the Question -}}}$

• (2x + 7) = 9
• (5x + 7) = 19

$\rule{300}{1.5}$

★ $\boxed{\tt{\frac{(2x + 7)}{(5x + 7)} = \frac{9}{19}}}$

$\tt{\longrightarrow} \: \dfrac{(2x + 7)}{(5x + 7)} = \dfrac{9}{19}$

$\tt{\longrightarrow} \:19(2x + 7) = 9(5x + 7)$

$\tt{\longrightarrow} \:38x + 133 = 45x + 63$

$\tt{\longrightarrow} \:38x - 45x = 63 - 113$

$\tt{\longrightarrow} \:\cancel - \: 7x = \cancel - \: 70$

$\tt{\longrightarrow} \:x = \dfrac{70}{7}$

$\tt{\longrightarrow} \:x = 10$

$\rule{300}{1.5}$

★ Value of 2x

$\tt{\longrightarrow} \:2 \times 10$

$\tt{\longrightarrow} \:20$

One Number = 20

$\rule{300}{1.5}$

★ Value of 5x

$\tt{\longrightarrow} \:5 \times 10$

$\tt{\longrightarrow} \:50$

Second Number = 50

$\therefore$ The two numbers are 20 and 50.

$\rule{300}{1.5}$

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

$\tt{\longrightarrow} \: \dfrac{20 + 7}{50 + 7} = \dfrac{9}{19}$

$\tt{\longrightarrow} \: \dfrac{27 \div 3}{57 \div 3} = \dfrac{9}{19}$

$\tt{\longrightarrow} \: \dfrac{9}{19} = \dfrac{9}{19}$

$\therefore$ The two numbers are 20 and 50.

Answer 2

Answer:

The two numbers are 20 and 50.

Explanation:

Given :

The ratio of the Numbers = 2 : 5

The new ratio when 7 is added to them = 9 : 19

To Find :

The Numbers.

Solution :

→ Consider the Original Numbers as:

• 2x
• 5x

→ According to the Question:

• (2x + 7) = 9
• (5x + 7) = 19

$\boxed{\tt{\frac{(2x + 7)}{(5x + 7)} = \frac{9}{19}}}$

$\tt{\longrightarrow} \: \dfrac{(2x + 7)}{(5x + 7)} = \dfrac{9}{19}$

$\tt{\longrightarrow} \:19(2x + 7) = 9(5x + 7)$

$\tt{\longrightarrow} \:38x + 133 = 45x + 63$

$\tt{\longrightarrow} \:38x - 45x = 63 - 113$

$\tt{\longrightarrow} \:\cancel - \: 7x = \cancel - \: 7x$

$\tt{\longrightarrow} \:x = \dfrac{70}{7}$

$\tt{\longrightarrow} \:x = 10$

→ Value of 2x

$\tt{\longrightarrow} \:2 \times 10$

$\tt{\longrightarrow} \:20$

One Number = 20

→ Value of 5x

$\tt{\longrightarrow} \:5 \times 10$

$\tt{\longrightarrow} \:50$

Second Number = 50

∴ The two numbers are 20 and 50.