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the sum of the digits of a two digit number is 12 , if the new number formed by reversing the digits is greater than the original number by 54, find the original number.

meritnation expert please answer to this qusstion as i am having my exams on sunday pls

Let the digit at one's place = x

digit at ten's place = 12 - x

Original number = 10(12 - x) + x = 120 - 9x

When the digits are reversed, then new number = 10x + (12 - x) = 9x + 12

According to the given condition, 

9x + 12 = 120 - 9x + 54

⇒ 18x = 162 ⇒ x = 162 / 18  = 9

so, original number = 120 - 9 × 9 = 120 - 81 = 39

So, the answer is 39

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Let x and y be the numbers,

x+y=12

Old Number= x+y Where as New Number=y+x

y+xx+y

(y+x-12)-(x+y-12)=54

2x+y-12=54

By transporting 12 to the other side we get:

2x+y=54+12 (Here this is +12 because on the other side the sign was negative when we transport it becomes positive)

2x+y=186

xy=186/2=93

So, 9+3=12 And When we reverse the number we get 39 Which is the old number. I conclude by telling that:

New Number=93

Old Number=39

9+3=12, 93-54=39 or 34+54=93.

Thumbs Up If it helped you.

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In they+xx+y place i meant y+x x+y

Sorry for the Wrong Mistake.

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I actually meant y+x is greater than x+y

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Let x and y be the numbers,

x+y=12

Old Number= x+y Where as New Number=y+x

y+xx+y

(y+x-12)-(x+y-12)=54

2x+y-12=54

By transporting 12 to the other side we get:

2x+y=54+12 (Here this is +12 because on the other side the sign was negative when we transport it becomes positive)

2x+y=186

xy=186/2=93

So, 9+3=12 And When we reverse the number we get 39 Which is the old number. I conclude by telling that:

New Number=93

Old Number=39

9+3=12, 93-54=39 or 34+54=93.

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tej singh I think you have just copy pasted from sneha ' s answer as its a replica

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Yeah, That's Rught Shantha. Tej Singh has just copy pasted my answer.

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I meant Right

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