Question

Two numbers are in ratio 5:9 The sum of Numbers is 280 Find both numbers

Answer 1

$\huge\mathfrak\blue{Answer:}$

Given:

• We have been given two numbers they are in ratio 5:9
• Sum of Numbers is 280

To Find:

• We have to find the Numbers

Solution:

Let First number = 5x

Second number = 9x

According to the Question

$\implies$ Sum of numbers = 280

$\implies$ 5x + 9x = 280

$\implies$ 14x = 280

$\implies$ x = $\dfrac{280}{14}$

$\implies$ x = 20

_______________________________

First number ( 5x ) = 100

Second Number ( 9x ) = 180

Two numbers are 100 and 180

_______________________________

Verification:

$\fbox{Ratio = \dfrac{100}{180} = \dfrac{5}{9}}$

$\fbox{ Sum = 100 + 180 = 280 }$

Hence Verified !!

Answer 2

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Given:

• It is given that the ratio of two numbers is 5 : 9.
• The sum of numbers is 280.

To Find:

• We need to find both numbers.

Solution:

The given ratio of numbers is 5 : 9.

Let the numbers be 5x and 9x.

According to the question, we have

$\longrightarrow\sf{ 5x + 9x = 280}$

$\longrightarrow\sf{ 14x = 280}$

$\longrightarrow\sf{ x = \dfrac{280}{14} }$

$\longrightarrow\sf{ x = 20}$

Now, numbers are:

$\mapsto\sf{ 5x = 5 \times 20 = 100}$

$\mapsto\sf{ 9x = 9 \times 20 = 180}$

Verification:

Sum:

$\mapsto\sf{ 100 + 180 = 280}$

Ratio:

$\mapsto\sf{\dfrac{100}{180} = \dfrac{5}{9}}$

Hence verified!!

Therefore, the required numbers are 100 and 180.