Question

3 A number is divided into two parts
such that one part is 5 less than the
other. If the two parts are in the rational
5:4, find the number and the two
parts.​

Answer 1

QUESTION :-

A number is divided into  two parts such that one part is 5 less than the other. If the two parts are in the ratio 5:4 , find the number and  the two parts.

SOLUTION :-

Let the number be n .

according to the question - it is divided into two parts

assuming the one part to be x  , then as given in the question the other part is equal to  ( x- 5 ).

✒  ratio of the two parts = 5:4

${\sf{\red{\frac{x}{x-5} =\frac{5}{4}}}}$

${\implies{\sf{\red{4x=5(x-5)}}}}$

${\implies{\red{\sf{4x=5x-25}}}}$

${\implies{\red{\sf{5x-4x=25}}}}$

${\implies{\sf{\red{x=25}}}}$

therefore,

first part = x = 25

other part = x -5 = 25- 5 = 20

the number , (n) = x + x- 25  = 25+20  =  45

Answer 2

Question:

A number is divided into two parts such that one part is 5 less than the other. If the two parts are in the ratio 5:4 , find the number and the two parts.

To find:

★ To find the number.

Answer:

$The \: number \: is \: \underline{ \: \underline{ \: \: \sf \pink{\bold{ 45}} \: \: } \: }$

Given:

✴ A number is divided into two parts.

✴ ${2}^{nd}$ part is 5 less than the other.

✴ Ratio of the two parts = 5:4

Step by step explanation:

Let the number be x .

Now assumption ,

Let the one part be y

Let the other part be y - 5

( one part is 5 less than the other )

The number ( x ) = y + ( y - 5 )

$The \: number \: \underline{ \: ( x ) = 2y - 5 \: }$

Ratio of the two parts is 5:4

$\implies \dfrac{y}{y - 5} = \dfrac{5}{4}$

$\implies 4(y) = 5(y - 5)$

$\implies 4y = 5y - 25$

$\implies 5y- 4y = 25$

$\implies \boxed{ y = 25}$

$\longmapsto$ The number ( x ) = 2y - 5

$\longmapsto x = 2(25)-5$

$\longmapsto x = 50-5$

$\longmapsto \boxed{ x = 45}$

$\therefore The \: number \: is \: \underline{ \: \: \bold{ 45} \: \: }$