Question

divide 4000 in two parts in the ratio 5:3​

Answer 1

$\Large {\underline { \sf {Clarification :}}}$

Here, we have to divide 4000 in two parts in the ratio 5:3. So, we'll assume the two parts as 5x and 3x respectively. x is a constant natural number here. Then, by forming a linear equation and solving that equation by using Transposition Method, we'll find the value x. After that, we'll multiply the value of x with 5 and 3 to find the two parts.

$\bf \red { \dag }$ Transposition Method :

• This is the method used to solve a linear equation having variables and constants.
• In this method, we transpose the values from R.H.S to L.H.S and vice-versa and changes its sign while transposing to find the value of the unknown value.

$\Large {\underline { \sf {Explication\: of \: Steps :}}}$

Let,

• First part ⇒ 5x
• Second part ⇒ 3x

According to the question,

● 4000 has to be divided into two parts. So, the sum of two parts is equivalent to 4000. Let's write it in the form of a linear equation.

$\longrightarrow \sf { First \: Part + Second \: Part = 4000 }$

$\longrightarrow \sf { 5x + 3x = 4000 }$

Performing addition.

$\longrightarrow \sf { 8x = 4000 }$

Transposing 8 from L.H.S to R.H.S. It's sign will be changed, i.e in L.H.S it is in the form of multiplication with x. So, in R.H.S it'll be in the form of division with 4000.

$\longrightarrow \sf { x = \dfrac{4000}{8} }$

$\longrightarrow \sf { x = 500 }$

Now, finding those two parts :

• First part ⇒ 5x

$\implies \sf { First \: part = 5(500) }$

$\implies \sf \red { First \: part = 2500 }$

• Second part ⇒ 3x

$\implies \sf { Second \: part = 3(500) }$

$\implies \sf \red { Second \: part = 1500 }$

Hence, we divided 4000 in two parts in the ratio 5:3 !