Question

Two numbers are in the ratio of 5:6. If 9 is added to each of them the ratio becomes 6:11. Find the numbers.​

Answer 1

$\LARGE{ \underline{ \orange{ \sf{Required \: answer:}}}}$

Given in the question, the ratio of two numbers is 5 : 6, So we can consider these numbers be 5x and 6x.

Now, 9 is added to the numbers. And the new numbers are in the ratio of 6 : 11.

That means,

➝ $\sf{ \dfrac{5x + 9}{6x + 9} = \dfrac{6}{11} }$

Cross multiplying,

➝ $\sf{11(5x + 9) = 6(6x + 9)}$

Now expanding the parentheses,

➝ $\sf{55x + 99 = 36x + 54}$

Isolating x in any one of the equation,

➝ $\sf{55x - 36x = 54 - 99}$

➝ $\sf{19x = - 45}$

Dividing 19 from both sides of the equation,

➝ $\sf{x = \dfrac{ - 45}{19} }$

Then the required numbers are:

• 5x = -225 / 19
• 6x = -270 / 19

And we are done !!

Answer 2

Answer:

✳️ Given ✳️

$\mapsto$ Two numbers are in the ratio of 5:6. If 9 is added to each of them the ratio become 6:11.

✳️ To Find ✳️

$\mapsto$ What is the numbers.

✳️ Solution ✳️

✒️ Let the rational between two numbers be x

✒️ Two numbers are in a ratio 5:6. Hence, the numbers are 5x and 6x. If 9 is added to each number, we get a new ratio of 6:11.

✒️ On adding 9 the two numbers become 5x + 9 and 6x + 9.

➕ According to the question,

$\implies$ $\dfrac{5x + 9}{6x + 9}$ = $\dfrac{6}{11}$

✍️ By doing cross multiplication we get,

$\implies$ 11(5x + 9) = 6(6x + 9)

$\implies$ 55x + 99 = 36x + 54

$\implies$ 55x - 36x = 54 - 99

$\implies$ 19x = - 45

$\implies$ x = $\dfrac{- 45}{19}$

✏️ The rational number is $\dfrac{- 45}{19}$.

$\therefore$ The numbers are,

$\dashrightarrow$ 5x = 5 × $\dfrac{- 45}{19}$ = $\dfrac{- 225}{19}$ $\green\bigstar$

$\dashrightarrow$ 6x = 6 × $\dfrac{- 45}{19}$ = $\dfrac{- 270}{19}$ $\green\bigstar$

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