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
and the two parts​

Answer 1

Answer :-

• The number is 40.
• The two parts are 15 and 25.

Step-by-step explanation:

To Find:-

• The number
• The two parts

Solution:

Given that,

• A number is divided into two parts, one part is 10 more than the other.
• The two parts are in the ratio of 5:3

Assumption:

Let us assume,

• One part of the number as ( x ).
• Other part of the number which is 10 more than the other as ( x + 10 ).

According the question,

$\sf{\dfrac{x + 10}{x} = \dfrac{5}{3}}$

By simplifying,

$\implies \: \sf{\dfrac{x + 10}{x} = \dfrac{5}{3}}$

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

$\implies \: \sf{3x + 30 = 5x}$

$\implies \: \sf{3x - 5x = - 30}$

$\implies \: \sf{- 2x = - 30}$

$\implies \: \sf{2x = 30}$

$\implies \: \sf{x = \dfrac{30}{2}}$

$\implies \: \sf{x = \cancel{\dfrac{30}{2}}}$

$\implies \: \sf{x = 15}$

We got, the value of x = 15. Therefore,

The parts are :-

• The part which we assumed as ( x ).

$\implies \: \sf{( x )}$

$\implies \: \boxed{ \sf{15}}$

• The part which we assumed as ( x + 10 ).

$\implies \: \sf{( x + 10 )}$

$\implies \: \sf{( 15 + 10 )}$

$\implies \: \boxed{ \sf{25}}$

Now, The Number is :-

$\longrightarrow \: \sf{25 + 15}$

$\longrightarrow \: \sf{40}$

Answer 2

Answer :-

1. The resultant number = 40.
2. Two parts obtained = 25 and 15.

Step by step explanation :-

Given :-

1. First part is the 10 more than the second part.
2. Ratio between the two parts = 5:3.

To find :-

1. Two parts of the number.
2. Number obtained from the two parts.

Concept :-

• Assumption of any one part of the nunber and then taking the other part according to the first assumed part.

• Taking the resultant assumed part equal to the ratio 5:3 to find the value first part and then finding the value of second part from the first part.

• Summing up both the parts for finding out the required number.

Solution :-

Let the first part be y.

∴ Value of other part = y+10

• ( Since, it is given that the second part is 10 more than the first. )

Now, the given ratio is 5:3.

According to the question :-

Relationship between the parts and the ratio :-

(y+10)/y = 5/3

• On cross-muliplying.

⇒ 3(y+10) = 5(y)

• Removing brackets according to the rule of BODMAS.

⇒ 3y + 30 = 5y

⇒ 30 = 5y - 3y

⇒ 30 = 2y

⇒ y = 30/2 = 15.

∴ First part of the number = y = 15

And, second part = y+10 = 15+10 = 25

Resultant Number = y + y + 10 = 15 + 25 = 40.