Question

A Number is divided into two parts such that one part is 10 more than the other .if the two parts are in the ratio 5:3 find the numbers.
[HINTS] Let one number be x , then be x +10. According to the problem,
x+10/x = 5/3 or (x+10)=5x]
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Answer 1

Question :

A Number is divided into two parts such that one part is 10 more than the other .if the two parts are in the ratio 5:3 find the numbers.

Given :

• A number is divided into two parts such that one part is 10 more than another
• They are in the ratio of 5 : 3

To find :

• The numbers (two parts)

Solution :

Let the smaller part be m

∴ Bigger part = (m + 10)

Now according to question,

⇒ (m + 10) : m = 5 : 3

⇒ (m + 10)/m = 5/3

⇒ 5m = 3(m + 10)

⇒ 5m = 3m + 30

⇒ 5m - 3m = 30

⇒ 2m = 30

⇒ m = 30/2

⇒ m = 15

∴ Smaller part = m = 15

∴ Bigger part = m + 10 = 15 + 10 = 25

Therefore,

The numbers are 25 and 15 respectively.

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Verification :

Bigger part : Smaller part = 5 : 3

25 : 15 = 5 : 3

5 : 3 = 5 : 3                     [Hence verified]

Answer 2

Answer :-

$\:\:\:\underline{\boxed{\sf{\red{Understanding \: the \: \bf{Concept} \:}}}}$

Here the concept of Linear Equations in One Variable has been used. According to this, the value of the variable is made to depend on the constant terms. In this way we find the value of variable.

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★ Question :-

A number is divided into two parts such that one part is 10 more than the other . If the two parts are in the ratio 5:3, find the numbers.

★ Solution :-

Given,

» One part is more than the other part by 10.

» Ratio of the two parts = 5 : 3

• Let the smaller part be x.

• Then the larger part will be (x + 10).

Now we surely know that the bigger part will be 5k and smaller part will be 3k from ratio 5:3 where k is a constant.

Now let us combine the given things with the variables we formed.

According to the question,

$\: \: \Longrightarrow \: \: \bold{\dfrac{x \: + \: 10}{x} \: = \: \dfrac{5}{3}}$

✒ 3 × (x + 10) = 5 × x

✒ 3x + 30 = 5x

✒ 5x - 3x = 30

✒ 2x = 30

$\: \: \Longrightarrow \: \: \bold{x \: = \: \dfrac{30}{2}}$

✒ x = 15

So, the numbers are :-

✏ Bigger number = x + 10 = 10 + 15 = 25

✏ Smaller number = x = 15

So,

$\:\:\:\underline{\boxed{\sf{\blue{The \: bigger \: number \: is \: \underline{25} \: and \: the \: smaller \: number \: is \: \underline{15} \: \:}}}}$

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$\:\:\: {\boxed{\tt{\pink{Confused ?\: Don't \: worry \: , \: let \: us \: verify \: - \:}}}}$

For verification of the number we mist simply have to equate the values we got into our equation. So,

➠ (x + 10) / x = 5 / 3

➠ (15 + 10) / 15 = 5 / 3

➠ 25 / 15 = 5 / 3

➠ 3 × 25 = 15 × 5

➠ 75 = 75

Clearly, LHS = RHS, hence our answer is correct.

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$\:\:\:\underline{\boxed{\rm{\green{Please, \: Refer \: to \: Supplementary \: Shots \: !!\:}}}}$

• Linear Equation is a type of polynomial which is formed using constant and variable terms. Its degree is always one.

• On the basis of degree of polynomial, they are divided into :-

1. Linear Polynomial / Constant Polynomial with highest degree 1 .
2. Quadratic Polynomial with highest degree of 2.
3. Cubic Polynomial with highest degree of 3.
4. Bi - Quadratic Polynomial with highest degree of 4.