Question

A number consists of two digits whose sum is 9. If 27 is subtracted from the number its digits are reserved.find the number.
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Answer 1

Solution :-

Let :-

Digit in ten's place = x

Digit in one's place = y

Two digit number = 10x + y

According to the first condition :-

$\longrightarrow \sf x+y = 9 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .......................(1)$

According to the second condition :-

$\longrightarrow \sf 10x+y-27 = 10y+x \\\\\longrightarrow 10x-x+y-10y = 27 \\\\\longrightarrow 9x-9y = 27 \\\\\longrightarrow x-y = 3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ .......................(2)$

Add eq (1) and eq (2) :-

$\longrightarrow \sf 2x= 12 \\\\\longrightarrow \bf x = 6$

Substitute the value of x in eq (1) :-

$\longrightarrow \sf 6+y = 9 \\\\\longrightarrow \bf y = 3$

Two digit number = 63

Answer 2

$\huge\bold{\underline{Question:}}$

A number consists of two digits whose sum is 9. If 27 is subtracted from the number its digits are reversed .find the number.

$\huge\bold{\underline{Answer:}}$

GIVEN:

• number consists of two digits whose sum is 9.

• 27 is subtracted from the number its digits are reversed.

TO FIND:

Find the number.

SOLUTION:

Let us assume, ' x ' and ' y ' are the two digits of the two-digit number.

Therefore, the two-digit number = 10x + y

and reversed number = 10y + x

.°. x + y = 9 (given)...............➊

ATQ,

$\sf{:\implies 10x + y - 27 = 10y + x}$

$\sf{:\implies 10x - x + y - 10y = 27}$

$\sf{:\implies 9x - 9y = 27}$

$\sf{:\implies 9(x - y) = 27}$

$\sf{:\implies x - y = \dfrac{27}{9}}$

$\sf{:\implies x - y = 3}$.............➋

Adding equation (1) and equation (2)

$\sf{:\implies 2x = 12}$

$\boxed{\bf{\pink{⟹\:x\:=\:6}}}$

Now, put the value of ' x ' in equation (1)

$\sf{:\implies 6 + y = 9}$

$\boxed{\bf{\pink{⟹\:y\:=\:3}}}$

Hence,

The two-digit number = 10×6 + 3 = 63

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