Question

4. A number consists of two digit whose sum is 9.
If 9 is subtracted from the number the digits
interchange their places. Find the number,
5. A number consists of two digit of which ten's
digit exceeds the units digit by 6. The number
itself is equal to ten times the sum of its digits
Find the number.​

Answer 1

Answer

1 . 54

2 . 60

Given

1 . A number consists of two digit whose sum is 9.  If 9 is subtracted from the number the digits  interchange their places.

2 . A number consists of two digit of which ten's  digit exceeds the units digit by 6. The number  itself is equal to ten times the sum of its digits

To Find

Number

Solution

1 .

Let the two digit's number be , " 10 y + x "

A/c , " sum is 9 "

⇒ x + y = 9 ... (1)

A/c , " If 9 is subtracted from the number the digits  interchange their places "

⇒ ( 10y + x ) - 9 = ( 10x + y )

⇒ 10y + x - 10x - y = 9

⇒ 9y - 9x = 9

⇒ y - x = 1 ... (2)

On solving , (1) + (2) , we get ,

⇒ ( x + y ) + ( y - x ) = 9 + 1

⇒ x + y + y - x = 10

⇒ 2y = 10

⇒ y = 5

On sub. y value in (1) , we get ,

⇒ x = 9 - 5

⇒ x = 4

So , two digit's number = 10y + x

⇒ 10(5) + 4

⇒ 50 + 4

⇒ 54

2 .

Let the two digit's number be , " 10y + x "

A/c , " A number consists of two digit of which ten's  digit exceeds the units digit by 6 "

⇒ y = x + 6 ... (1)

A/c , "  The number  itself is equal to ten times the sum of its digits "

⇒ ( 10y + x ) = 10 ( x + y )

⇒ 10y + x = 10x + 10y

⇒ 10y + x - 10x - 10y = 0

⇒ -9x = 0

⇒ x = 0

On sub. x value in (1) , we get ,

⇒ y = 0 + 6

⇒ y = 6

So , two digit's number = 10y + x

⇒ 10(6) + 0

⇒ 60

Answer 2

Question:

1. A number consists of two digit whose sum is 9. If 9 is subtracted from the number the digits interchange their places. Find the number.

2. A number consists of two digit of which ten's digit exceeds the units digit by 6. The number itself is equal to ten times the sum of its digits.Find the number.

To find:

★ To find the numbers.

Answer:

1. 54 .

2. 60 .

Step-by-step explanation:

Solution for ${1}^{st}$ Question.

Let us assume,

The number be ‘ 10y + x ’ [ two digits ]

Also given, sum of the number is 9.

$\therefore x + y = 9 \: --->(1)$

9 is subtracted from the number =

(10y + x) - 9

The digits interchange their places = 10x + y

$\implies (10y + x) - 9 = 10x + y$

$\implies 10y - y = 10x - x + 9$

$\implies 9y = 9x + 9$

$\implies 9y - 9x = 9$

$\implies y - x = 1 \: --->(2)$

Adding ( 1 ) and ( 2 )

x + y = 9

- x + y = 1

_________

2y = 10

$\: \: \:\boxed{y=5}$

_________

Now substituting the value of y in ( 1 )

$\rightarrow x + 5 = 9$

$\rightarrow \boxed{x = 4}$

$\therefore$The required number is,

$\hookrightarrow 10(5) + 4$

$\hookrightarrow 50 + 4$

$\hookrightarrow \boxed{ \bf{5 4}}$

$\therefore$The number is 54 .

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Solution for ${2}^{nd}$ Question.

Let us assume,

The number be ‘ 10y + x ’ [ two digits ]

A number consists of two digit of which ten's

A number consists of two digit of which ten'sdigit exceeds the units digit by 6.

$\therefore y = x + 6 \: --->(1)$

The number itself is equal to ten times the sum of its digits.

$\longmapsto 10y + x = 10(x + y)$

$\longmapsto 10y + x = 10x + 10y$

$\longmapsto 10y + 10y+ x - 10x = 0$

$\longmapsto - 9x = 0$

$\longmapsto \boxed{x = 0}$

Now substituting the value of x in eq ( 1 )

$\leadsto y = 0 + 6$

$\leadsto \boxed{y = 6}$

The required number is,

$\Rightarrow \: 10(6) + 0$

$\Rightarrow \: \boxed{ \bf60}$

$\therefore$The number is 60 .

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⚠️Note⚠️

★ We have to read the question more than 2 times.

★ Because it forms the equation .

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