Question

What number must be added to each term of the
ratio 9 11, so that it becomes 4: 5.

Answer 1

$❒ \: \: { \underline{ \underline{ \textbf{\textsf{{ Given \::}{}}}}}}$

• What number must be added to each term of the ratio 9 : 11 so that it becomes 4 : 5.

$❒ \: \: { \underline{ \underline{ \textbf{\textsf{{ Solution \::}{}}}}}}$

Let the number must be added to each term of the ratio 9 : 11 be x.

❖ According to the question:

$\\ \\ ⇢ \tt \: 9 + x :11 + x = 4 : 5 \\ \\ \\ ⇢ \tt \: \frac{9 + x}{11 + x} = \frac{4}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

❖ By doing cross multiplication we get :

$\\ \\ ⇢ \tt \: 5(9 +x) = 4(11 + x) \\ \\ \\ ⇢ \tt \: 45 + 5x = 44 + 4x \\ \\ \\ ⇢ \tt \: 45 - 44 = 4x - 5x \\ \\ \\ \tt ⇢1 = - x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ ⇢ \tt \: - x = 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \\ \tt ⇢ \: { \underline{ \boxed{ \purple{ \pmb{ \mathfrak{x = - 1}}}}}} \: \bigstar \: \: \: \: \: \: \:$

• Hence, (-1) must be added to each term of the ratio 9 : 11 so that it becomes 4 : 5.

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Answer 2

Answer : x = -1

thank you, hope it helps......