P-1 Linear Equations in Two Variables — Maths STD 10 — Question

Solve the following word problems.
A two digit number and the number with digits interchanged add up to 143. In the given number the digit in unit’s place is 3 more than the digit in the ten’s place. Find the original number.
Let the digit in unit’s place is x
and that in the ten’s place is y
the number = ⬜y + x
The number obtained by interchanging the digits is ⬜x + y
According to first condition two digit number + the number obtained by interchanging the digits = 143
∴ 10y + x = 143
∴ ⬜x + ⬜y = 143
x + y = ⬜......(I)
From the second condition,
digit in unit’s place = digit in the ten’s place + 3
∴ X = ⬜ + 3
∴ X - Y= 3.....(II)
Adding equations (I) and (II)
2X = ⬜
X = 8
Putting this value of x in equation (I)
x + y = 13
8 + ⬜ = 13
∴ Y = ⬜
The original number is 10
= ⬜ + 8
= 58