Question

A number of two digits whose sum is 8. If 8 is subtracted from the number ,the digit interchange their places the number is?

Answer 1

Correct Question :

• A number of two digits whose sum is 8. If 18 is subtracted from the number ,the digit interchange their places the number is?

$\rule{200}1$

Given,

• Sum of two digits number is 8.
• when 18 is subtracted from the number then the digits interchange their place .

To Find,

• The Two Digit Number

Solution,

⇒Suppose the digit at the ten's place be a

And, Suppose the digit at the one's place be b

Therefore,

• Two Digit Number = 10a + b
• Interchange Number = 10b + a

According to the First Condition :-

• Sum of two digits number is 8.

$\implies \sf{a + b = 8}$

$\implies \boxed{\sf{b = 8 - a}}$

According to the Second Condition :-

• when 18 is subtracted from the number then the digits interchange their place .

$\implies \sf{10a + b - 18 = 10b + a}$

$\implies \sf{10a - a = 10b - b + 18}$

$\implies \sf{9a = 9b + 18}$

$\implies \sf{9a = 9(8 - a) + 18 }$

(Put the value of b from the First Condition)

$\implies \sf{9a = 72 - 9a + 18}$

$\implies \sf{9a + 9a = 90}$

$\implies \sf{18a = 90}$

$\implies \sf{a = \dfrac{90}{18}}$

$\implies \boxed{\sf{ a = 5}}$

Now Put the Value of a in First Condition :-

$\implies \sf{b = 8 - a}$

$\implies \sf{b = 8 - 5}$

$\implies \boxed{\sf{b = 3}}$

Therefore ,

$\large{\boxed{\bold{Two \ Digit \ number :=\:10x+y\:=\:10(5)+3=50+3=53}}}$

$\rule{200}2$

Answer 2

☯ Question:

A number of two digits whose sum is 8. If 8 is subtracted from the number ,the digit interchange their places the number is?

☯ Answer:

• Ten's digit = 5
• Unit's digit = 3
• Original number = 53

☯ Explanation:

$\leadsto$Let the ten's digit = x

$\leadsto$Now, the unit's digit = (8 - x)

$\mapsto$Original number = 10x + (8 - x) = 10x + 8 - x = 9x + 8

$\mapsto$Interchanged number = 10(8 - x) + x = 80 - 10x + x = 80 - 9x

★ According To The Question:

$\leadsto$9x + 8 - 8 = 80 - 9x

$\leadsto$9x + 9x = 80 - 9x

$\leadsto$18x = 80

$\leadsto$x = 80/18

$\bold\mapsto$x = 5

★ Now:

$\mapsto$Unit's digit = (8 - x) = (8 - 5) = 3

★ Final Answer:

$\longrightarrow$The number : We will put the value of x in 10x + (8 - x) :-

$\leadsto$10(5) + (8 - 5)

$\leadsto$50 + 3

$\bold\mapsto$53

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