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 is the
original number?
​

Answer 1

ASSUMPTIONS :

1. The two digit number is a natural number.
2. the digits of the number are x and y
3. the original number is 10x + y.
4. x is greater than y.

GIVEN :

digits of a 2 digit number differ by 3.

∴ x - y = 3........(ii)

addition of the new no. and original number = 143.

SOLUTION :

The new no. formed by interchanging the digits = 10y + x.

new no. + original no. = 143

(10y + x) + (10x + y) = 143

10y + y + 10x + x = 143

11x + 11y = 143

11(x + y) =  143

x + y = 143/11

x + y = 13 ........(i)

Adding equations (i) and (ii) :

(x + x) + (y - y) = (3 + 13)

2x = 16

x = 16/2

x = 8

Replacing the value of x in eqn (i) :

8 - y = 3

y = 5

Since the original number is 10x + y

= (10 × 8) + 5

= 85

The original number is 85. (Ans

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.

Hope it helps you ❤️