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

Maharashtra BoardEnglish MediumSTD 10MathsP-1 Linear Equations in Two Variables3 Marks
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.
✓

Answer

Let the digit in unit's place is $x$ and that in the ten's place is $y$
$\therefore$ the number $=10 y + x$
The number obtained by interchanging the digits is $10 x + y$
According to first condition two digit number + the number obtained by interchanging the digits $=143$
$\therefore 10 y+x+10 x+y=143 $
$\therefore 11 x+11 y=143 $
$\therefore x+y=13 \ldots \ldots( I )$
From the second condition, digit in unit's place $=$ digit in the ten's place +3
$\therefore x = y +3$
$\therefore x-y=3$
Adding equations (I) and (II)
$2 x=16 $
$x=8$
Putting this value of $x$ in equation $(I)$
$x+y=13 $
$8+y=13$
$\therefore y=5$
The original number is 10
$\Rightarrow 50+8 $
$\Rightarrow 58$

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