## The sum of the digits of a two digit number is 12. if the digits are reversed, the new number is 12 less than twice the original number. Fin

Question

The sum of the digits of a two digit number is 12. if the digits are reversed, the new number is 12 less than twice the original number. Find the original number. The question is of simultaneous linear equation.

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2 weeks 2021-09-06T05:26:49+00:00 2 Answers 0 views 0

When you add two numbers and the number obtained by reversing the order of its digits is 165. If the both numbers differ by three, find the number. one number is X ,other X +3 , so X +(x +3) = 561 or 2X = 561-3 =558 . now X =558/2 =279 ,one is 279 , other is 279 +3 =282 , answer.

Original Number 57, New number 75.

Let x represent the “tens” digit

let y represent the “ones” digit

So the original number is 10x + y

the reversed number is 10y + x

10x + y + 18 = 10y + x This is the new number is 18 more than the original

x + y =12 This is the sum of the digits is 12

Isolate x in x + y = 12 subtract y from both sides. x = 12 – y

Substitute 12-y for every x in: 10x + y + 18 = 10y + x =>

10(12-y) + y + 18 = 10y + (12-y) Distribute the 10

120 -10y + y + 18 = 10y + 12 – y Combine like terms

138 – 9y = 9y + 12 Add 9y on both sides

138 = 18y + 12 Subtract 12 on both sides

126 = 18 y divide both sides by 18

7 = y

x = 12 – y => x = 12 – 7 => x = 5

Original Number 57, new number 75. Check 75 -57 = 18

2. Step-by-step explanation:

Given that the sum of 2 digit number is 12. If the digits are reversed, the new number is 12 less than twice the original number.

we have to find the two digit number.

Let the two-digit number is xy therefore the number becomes 10x+y

As the sum of 2 digit number is 12 that means

x+y=12 → (1)

Now, if the digits are reversed, the new number is 12 less than twice the original number.

10y+x=2(10x+y)-12

10y+x=20x+2y-12

19x-8y=12 → (2)

Solving (1) and (2), we get

(2)+8(1) ⇒

19x-8y+8x+8y=12+96

27x=108

x=\frac{108}{27}=4

x+y=12 ⇒ 4+y=12 ⇒ y=8

Hence, the number is xy=48