Question

digits are reversed. Find the number.
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 number and the two parts. with explaination​

Answer 1

Given:

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

• Two parts are in the ratio 5:3.

To calculate:

• The number and the two parts.

Calculation:

According to the question,

• Two parts are in the ratio of 5:3.

Let the first part be 5x and another part be 3x .Now, according to the question another part is 10 more than the other. So,

→ 5x = 3x + 10

Collecting all like terms.

→ 5x - 3x = 10

Performing substraction.

→ 2x = 10

Transposing 2 from LHS to RHS.

→ x = $\sf{\dfrac{10}{2}}$

Performing division.

→ $\boxed {\sf{x = 5}}$

Now, substituting the values in the two part :

• First part = 5x

→ First part = 5 × 5

→ First part = 25

• Another part = 3x

→ Another part = 5 × 3

→ Another part = 15

Now, we are also asked to find the original number. As the original number is divided into two parts and we got the parts, so the original number :

• Original number = First part + Another part

→ Original number = 5x + 3x

→ Original number = 25 + 15

→ Original number = 40

Required Answer :

• Two parts ⇒ 15 and 25
• Original number⇒ 40

Answer 2

To find:

• two numbers

Given:

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

• Two parts are in ratio of 5:3

Let:

• first part be 5x
• second part be 3x
• number = 5x + 3x

$\bigstar \underline{ \boldsymbol{According \: to \: question: }}$

$\to \sf first \: part = second \: part + 10$

How ?

As it is told that on part is 10 more than the other which means 1 number is 10 units more than 2 number. Remember it's not told 10 times, if it is then instead of adding here we will multiply 2 number with it.

Now put the values of 1 part and second part which we have supposed

$\to \sf 5x = 3x + 10$

$\to \sf 5x - 3x=10$

$\to \sf 2x=10$

$\to \sf x= \dfrac{10}{2}$

$\to \sf x= \dfrac{5 \times 2}{2}$

$\to \sf x= \dfrac{5 \times\cancel 2}{\cancel2}$

$\to \sf x= 5 \times 1$

$\to \underline{ \boxed{\sf x= 5 }}$

$\bigstar \boldsymbol {verification: }$

$\to \sf 5x = 3x + 10$

$\to \sf 5 \times 5= 3 \times 5+ 10$

$\to \sf 25= 15+ 10$

$\to \underline{ \boxed{\sf 25=2 5 }}$

$\gray{\Large\bf\dag LHS = RHS\dag}$

$\gray{ \bf Hence \: verified }$

Finally:

• 1 part = 5x
• 1 part = 5 × 5
• 1 part = 25

• 2 part = 3x
• 2 part = 3 × 5
• 2 part = 15

• number = 5x + 3x
• number = 5 × 5 + 3 × 15
• number = 25 + 15
• number = 40