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

Hi !!!
Digits of a two digit number differs by 3.

If the digits are interchanged, then new number formed is added to the actual digit, then the sum will be 143.
Let the tens place digit be p and unit place digit be q.
So, the actual number will be 10p + q

Digits after interchanging = 10q+p

It is given that their difference is 3.

So,p - q = 3 ... .......(i).

It is given that their sum is 143.

So, 10p + q + 10q + p = 143.

11p + 11q = 143....... (Taking out common)
p + q = 13... . ....(ii).

Adding equation (i) and (ii),
we get
p - q = 3
p + q = 13
---------------------
2p. =. 16

Hence, p = 8.
Putting value of p in equation (i).
p - q = 38 - q = 3q = 5.
Now, putting value of p and q in 10p + q...
we get
10(8) + 5 = 85.
Hence, the original number is 85.
Hope it helps......

Answer 2

Heya friend!
Here's ur answer!

Let the tens place digit be a and units place digit be b.
So, the actual number will be 10a + b
Digits after interchanging = 10b+a

a- b = 3 ....(i)

10a + b + 10b + a = 143

11a + 11b = 143

a+ b = 13....(ii)

Adding equation (i) and (ii)
we get :

2a =. 16
a= 8

Putting value of a in equation (i) we get:

a - b = 3
8 - b = 3
b = 8 - 3
b = 5

Putting value of a and b in 10a + b
we get :

10(8) + 5 = 85

The original number is 85.

Hope this helps!!☺
Thanks!!☺