Question

The sum of digits of a two-digit number is 15.If the new number formed by the changing the place of the digits is greater than the original number by 9 ' find the original number and check the solution also

Answer 1

$\bf{\huge{\underline{\boxed{\sf{\purple{Answer:}}}}}}$

$\bf{\underline{\underline{\sf{\green{Given:}}}}}$

• The sum of digits of a two-digit number is 15.
• If the new number formed by the changing the place of the digits is greater than the original number by 9

$\bf{\underline{\underline{\sf{\green{To\:find:}}}}}$

• The original number

$\bf{\underline{\underline{\sf{\green{Solution:}}}}}$

Let the digit in the tens place be x.

Let the digit in the units place be y.

Original Number = 10x + y

$\bf{\underline{\underline{\sf{\green{As\:per\:first\:condition:}}}}}$

• The sum of digits of a two-digit number is 15.

Representing the condition mathematically.

=> x + y = 15 ---> 1

$\bf{\underline{\underline{\sf{\green{As\:per\:second\:condition:}}}}}$

• If the new number formed by the changing the place of the digits is greater than the original number by 9

Reversed Number = 10y + x

Representing the second condition mathematically.

=> 10y + x = 10x + y + 9

=> 10x + y + 9 = 10y + x

=> 10x - x + 9 = 10y - y

=> 9x + 9 = 9y

=> 9x - 9y = - 9

=> 9 ( x - y) = - 9

=> x - y = $\large\frac{-9}{9}$

=> x - y = - 1

Solve equations 1 and 2 simultaneously by elimination method.

Add equation 1 to equation 2,

x + y = 15

x - y = - 1

-------------

2x = 14

=> x = $\large\frac{14}{2}$

=> x = 7

Substitute x = 7 in equation 2,

=> x - y = - 1

=> 7 - y = - 1

=> - y = - 1 - 7

=> - y = - 8

=> y = 8

$\bf{\large{\underline{\boxed{\sf{\red{Digit\:in\:the\:tens\:place\:=\:x=\:7}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\red{Digit\:in\:the\:units\:place\:=\:y=\:8}}}}}}$

$\bf{\large{\underline{\boxed{\sf{\red{Original\:number\:=\:10x\:+\:y\:=\:10\:\times\:7\:+8\:=\:70\:+8\:=\:78}}}}}}$

Answer 2

Answer:

here your answer...........

Step-by-step explanation:

• let the tenth digit be a

• and unit' digit be b,

• then the number is 10a+b.

According to question

sum of two digits is 15

a+b=15

a+b-15=0...................................(1)

And

changing the digits the new number

formed greater than the original

number by 9

10b+a=10a+b+9

9a-9b+9=0

9(a-b+1)=0

a-b+1=0................................... (2)

now adding equations (1) and (2)

a+b-15+a-b+1=0

2a-14=0

2a=14

a=14/2

a=7.

substitute a value in equation (1)

7+b-15=0

b-8=0

b=8.

therefore the number is 10a+b

10×7+8=70+8=78.

verification:

the original number is 78

so,

according to question

sum of the digits is 15

7+8=15 (verified)

and if interchange the digits the new

number formed greater than the

original number by 9

87=78+9.

Hence proved.