Question

The sum of two numbers is 85 and their difference is 65, then the numbers are

Answer 1

$\mathfrak{\large{\underline{\underline{Answer: }}}}$

The Numbers are 10 and 75.

$\mathfrak{\large{\underline{\underline{Step-by-step \:explanation: }}}}$

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

Sum of the two numbers = 85

Their difference = 65

$\textsf{\underline{\underline{To find : }}}$

The Numbers

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

✯ $\textbf{\small{\underline{Let the numbers be -}}}$

• One as x
• Another as y

✯ $\textbf{\small{\underline{It is given that - }}}$

• x + y = 85
• x - y = 65

$\sf{\longrightarrow} \: x + y = 85 \\\sf{\longrightarrow} \: x = 85 - y \: ....(Equation \: 1)$

$\rule{300}{1.5}$

Their difference is 65 -

$\sf{\longrightarrow} \: x - y = 65 \\ \sf{\longrightarrow} \: \gray{Place \: the \: value \: of \: x \: from \: (Eq.1)} \\ \sf{\longrightarrow} \: (85 - y) - y = 65 \\ \sf{\longrightarrow} \: 85 - 2y = 65 \\ \sf{\longrightarrow} \: - 2y = 65 - 85 \\ \sf{\longrightarrow} \: \cancel- 2y = \cancel - 20 \\ \sf{\longrightarrow} \: y = 20 \div 2 \\ \sf{\longrightarrow} \: y = 10$

One Number = 10

$\rule{300}{1.5}$

★ Another Number -

$\sf{\longrightarrow} \: x = 85 - y \\ \sf{\longrightarrow} \: x = 85 - 10 \\ \sf{\longrightarrow} \: x = 75$

Another number = 75

$\therefore$ The Numbers are 10 and 75.

Answer 2

Answer:

Step-by-step explanation:

Given :-

The sum of two numbers is 85 and their difference is 65.

To Find :-

The Numbers.

Solution :-

Let the 1st number be x.

And the 2nd number be y.

According to the Question,

Sum of two numbers is 85

1st Equation

⇒ x + y = 85 .... (i)

2nd Equation

Difference of two numbers is 65

⇒ x - y = 65  .....(ii)

Solving Eq i(i) and (ii), we get

⇒ 2x = 20

⇒ x = 20/2

⇒ x = 2

Putting x value in Eq (i), we get

⇒ x + y = 85

⇒ 10 + y = 85

⇒ y = 85 - 10

⇒ y = 75

Hence, the numbers are 10 and 75.