Question

Q6. A number consist of 2 digits whose sum is 5.If 9 is added to the number the digits are
inte changed. Find the number​

Answer 1

Step-by-step explanation:

MATHS

A number consists of two digits whose sum is five. When the digits are reversed, the number becomes greater by nine. Find the number.

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ANSWER

Let the digits in the tens be x and ones place be y.

Hence the number is 10x+y

By reversing 10y+x

Sum of digit =5

⇒x+y=5⟶(i)

Also that when 9 is added to the number the digits get interchanged.

∴(10x+y)+9=(10y+x)

10x+y+9=10y+x=0

9x−9y=−9

x−y=−1⟶(ii)

Adding (i) &(ii) we get ,

⇒x+y=5

⇒x−y=−1

⇒2x=4

⇒x=2

Put x=2 in x+y=5

∴2+y=5

⇒y=3

Hence the no: is 23.

Answer 2

Answer:

let the no at one's place be 'y' and at tens place 'x'

then no will be (10x+y)

A/Q x+y = 5 .......(1)

10x+y + 9 = 10y+x

9x-9y=-9

x-y = -1 ......(2)

Adding eqn (1) nd (2) we get

x=2

putting this value in eqn (1)

x+y=5

2+y=5

y=5-2=3

Hence, the required answer is 10×2+3=23.

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