Question

the digits of a two digit number differ by 3 if the digits are interchanged and the resulting number is added to the original number we get 143 what can be the original number

Answer 1

Let the digits of the no. be x and y
according to the question x - y = 3 -------1)
Let the no. be 10x + y
No. obtained when the digits are reversed = 10y + x
Now,
10x + y + 10y + x = 143
11x + 11y = 143
11 ( x + y) = 143
x + y = 143 ÷ 11
x + y = 13 --------2)
x = 3 + y -----------3)
substituting the value of equation 3 in equation 2
3 + y + y = 13
2y = 13 - 3
2y = 10
y = 5
x + y = 13
x + 5 = 13
x = 13 - 5
x = 8
So the original no is 85.

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Answer 2

Solve:-

According to question ❓:-

Take , for example , a 2 digit number , say, 56.

Take , for example , a 2 digit number , say, 56. It can be written as 56 = (10 × 5) + 6.

~If the digits in 56 are interchanged , We get 65 , which can be written as (10×6) + 5.

• Let us take the two digit number such that the digit in the unit place is b.

• The digit in the tens place is different from b by 3.

• Let us take it as b + 3.

• So the two digit number is 10 (b+3) + b

= 10b + 30 + b

= 11b + 30

With interchange the digits , the resulting two number will be

= 10b + (b+3) = 11b + 3

If we add these two two digit numbers , their sum is

(11b + 30) + (11b + 3) = 11b + 11b + 30 + 3

= 22b + 33

It is given that the sum is 143.

Therefore , 22b + 33 = 143

• 22b = 143 - 33

• 22b = 110

• b = 110/22

• b = 5

Now,

Unit place = b

The value of b is 5 .

So, The unit place is 5.

Unit place = 5

Tens place = b + 3

So , We have to sum the both numbers.

Value of b = 5

So ,

b + 3

= 5 + 3

= 8

hence,

the number is 85.

Answer is verified.

Answering check ✅ => On interchange of digits the number we get is 58.

The sum of 85 and 58 is 143 are given.

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