Question

A two digit number is 3 more than 4 times the sum of its digit.If 18 is added to this number, the sum is equal to the number obtained by interchanging the digits.find the number.

Answer 1

Let the digit in ones place be x and tens place be y
Original number = 10y + x
Number formed by reversing the digits = 10x + y
Given 10y + x = 4(x + y) + 3
⇒ 10y + x − 4x − 4y = 3
⇒ 6y� − 3x� = 3
⇒ 2y� − x� = 1 → (1)
Also given that when 18 is added to the number the digits gets interchanged.
Hence (10y + x) + 18 = 10x + y
⇒ 9x − 9y = 18
⇒ x − y = 2� → (2)
Add (1) and (2), we get
2y� − x� = 1
x − y = 2
---------------
y = 3
Put y=3 in x − y = 2, we get
x − 3 = 2
∴ x = 5
Hence (10y + x) = 10(3) + 5 = 35

Answer 2

Let ,
unit digit = x
Tens digit = y
Number = 10x + y
10x + y= 4(x + y) + 3
10x + y = 4x +4y + 3
10x - 4x + y - 4y = 3
6x - 3y. = 3
2x - y = 1. ..........(1)
A/q
10x + y + 18 = 10y + x
10 x - x + y -10y = - 18
9x - 9y = -18
x - y = -2. ------(2)
equation (1) - equation (2)
2x - y = 1
x - y = -2
- + +
_________
x = 3
in equation (1) we put x = 3
2x - y = 1
2×3 - y = 1
6 - y. = 1
- y = 1- 6
y = 5
Number = 10x + y
= 10 × 3 + 5
= 35
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