Question

the sum of the digits of a two digit number is 9.If 9 is added to the numberby reversing its digits,then the result is thrice the original number.find the original number
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Answer 1

Given,

• The Sum of the Digits of a two Digit number is 9.
• If 9 is added to the number by reversing its digits then the result is thrice the original number.

To Find,

• The Two Digit Number

Solution :

$\implies$ Suppose the digit at the ten's place be x

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

Therefore,

• Two Digit Number = 10x + y
• Reversing Number = 10y + x

$\mapsto \underline{\sf{\pink{According \ to \ the \ First \ Condition :}}}$

• The sum of the digits of a two digit number is 9.

$\longrightarrow \sf{x + y = 9}$

$\longrightarrow \boxed{\sf{x = 9 - y}}$   1) Equation

$\mapsto \underline{\sf{\pink{According \ to \ the \ Second \ Condition :}}}$

• If 9 is added to the number by reversing its digits,then the result is thrice the original number.

$\longrightarrow \sf{3(10x + y) = 10y + x + 9}$

$\longrightarrow \sf{30x + 3y = 10y + x + 9}$

$\longrightarrow \sf{30x - x = 10y - 3y + 9}$

$\longrightarrow \sf{29x = 7y + 9}$

║Now Put the Value of x From the Equation First ║

$\longrightarrow \sf{29(9 - y) = 7y + 9}$

$\longrightarrow \sf{261 - 29y = 7y + 9}$

$\longrightarrow \sf{261 - 9 = 7y + 29y}$

$\longrightarrow \sf{252 = 36y}$

$\longrightarrow \sf{y = \dfrac{252}{36}}$

$\longrightarrow \boxed{\sf{y = 7}}$

║Now Put the Value of y in First Equation ║

$\longrightarrow \sf{x = 9 -y}$

$\longrightarrow \sf{x = 9 - 7}$

$\longrightarrow \boxed{\sf{x = 2}}$

Therefore,

$\boxed{\bold{\red{Two \ Digit \ Number = 10x + y = 10(2) + 7 = 27}}}$

$\rule{200}2$

Answer 2

Answer:

Step-by-step explanation:

Let no. in the ones place be x and no.in the tens place be y.

Original no.=x+10y

A/q

x+y=9

=> x=9-y

Also,

(10x+y)+9=3(x+10y)

=> (10(9-y))+9=3(9-y+10y)

=> 90+10y+9=27+27y

=> 99+10y=27+27y

=> 99+10y-27-27y=0

=> 72-36y=0

=> y=72/36

y=2

Therefore

x=9-y

=7

Therefore the number is:

x+10y

=7+10x2

=27...ans