The digit of two-digit number differ by 3. If digits are interchanged, and the resulting number is added to the original number, we get 143. Find the original number.
Answers
Answer:
number is 85
Step-by-step explanation:
let the tens digit = x
and once digit = y
A.T.Q
x - y = 3 -------(1)
number is the form 10x + y
if interchanging the digit
tnen new number is 10y + x
10x + y + 10y + x = 143
11x + 11y = 143
divide by 11
x + y = 13 --------------(2)
on adding eq 1 and 2
x - y = 3
x + y = 13
2x = 16
x = 16/2
x = 8
put x in eq 2
x + y = 13
8 + y = 13
y = 13 - 8
y = 5
number is 10x + y = 10 × 8 + 5
= 80 + 5 = 85
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 ❤️