Question

Two numbers are in the ratio 5:3 if they differ by 18 whar are the numbers​

Answer 1

${ \textbf{\textsf{ \underline{ \underline{\quad{Given :}{\quad}}}}}}$

• Two numbers are in the ratio 5:3. If they differ by 18 what are the numbers?

${ \textbf{\textsf{ \underline{ \underline{\quad{Solution \: :}{\quad}}}}}}$

Let the two numbers be 5y and 3y.

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

$\\ \tt \therefore \: \: \: \: 5y - 3y = 18 \\ \\ \\ \tt⇢ \: \: \: \: 2y = 18 \\ \\ \\ ⇢ \: \: \: \: \: \: \tt \: y = \frac{18}{2} \\ \\ \\ \tt ⇢ \: \: \: \: \: \: y = 9$

Hence, The value of y = 9.

$\\ ⇢ { \textbf{ \textsf{First number}}} = \tt 5y \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \tt \: 5 \times 9\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \tt \:45$

$\\ ⇢ { \textbf{ \textsf{Second number}}} = \tt 3y \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \tt \: 3 \times 9\\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = \tt \:27$

${\textbf{\textsf{ { {So, The two numbers are}}}}} \: \: {\purple{\mathfrak{45 \: and \: 27}}}.$

Answer 2

Answer :-

The numbers are 45 and 27.

Step-by-step explanation

To Find :-

• The numbers.

★ Solution

Given that,

• Two numbers are in the ratio of 5:3
• The two numbers differ by 18.

Assumption

Let us assume the numbers as 5x and 3x.

ATQ,

• 5x - 3x = 18

On solving them,

→ 5x - 3x = 18

→ 2x = 18

→ x = 18/2

→ x = 9

The value of x = 9.

Now, The numbers are :-

• 5x = 5*9 = 45
• 3x = 3*9 = 27

Hence, The numbers are 45 and 27.

_________________________________

Verification

• 5x - 3x = 18

By putting the value of x, in LHS :-

→ 5x - 3x

→ 5*9 - 3*9

→ 45 - 27

→ 18

Now, LHS = RHS

Hence, Verified!