Question

A number is divided into two equal such one part is 10 more than the other. if the two parts are in the ratio 5:3 find the number and the two parts?

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Answer 1

Answer :-

• 1st part = x = 15.

• 2nd part = x + 10 = 25.

• Number = 40.

Explanation :-

Given :

• A number is divided into two equal such one part is 10 more than the other.

• The two parts are in the ratio 5:3.

To Find :

• The Number and the two parts.

Solution :

Let one part of the number be x.

So, The Other part will be x + 10.

★ According to the Question,

⇢ (x + 10)/x = 5/3.

⇢ 3(x + 10) = 5(x).

⇢ 3x + 30 = 5x.

⇢ 5x - 3x = 30.

⇢ 2x = 30.

⇢ x = 30 ÷ 2.

⇢ x = 15.

Therefore,

• 1st part = x = 15.
• 2nd part = x + 10 = 25.

And,

The Number = 1st part + 2nd Part.

⇢ Number = 15 + 25.

⇢ Number = 40.

Hence, The Number = 40.

Answer 2

AnswEr -:

• First part -: 15 .
• Second part -: 25 .
• The number is 40 .

Explanation -:

Given ,

• A number is divided into two parts such as one part is 10 more than the other.
• The two parts are in ratio 5:3 or $\sf{\frac{5}{3}}$

To Find ,

• The number and the two parts .

Solution,

• Let the first part be -: x .
• The second part is 10 more than the first part -: x + 10 .

According to the question,

$\sf{\rightarrow { \frac {x + 10} {x} = \frac{5}{3}}}$ [ Cross Multiplication]

$\sf{\rightarrow { 3(x+10) = 5(x)}}$

$\sf{\rightarrow { 3x + 30 = 5x}}$

$\sf{\rightarrow { 5x-3x = 30 }}$

$\sf{\rightarrow { 2x = 30 }}$

$\sf{\rightarrow { x =\frac {30}{2}}}$

$\sf{\rightarrow { x = 15 }}$

Therefore,

• First part -: x -: 15 .
• Second part -: x + 10 -: 15 + 10 = 25 .

☆ The number -: first part + second part

• First part-: 15
• Second part -: 25

=》25 + 15

=》40

Hence ,

• The number is 40 .

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