10th Class Mathematics Pair of Linear Equations in Two Variables Question Bank MCQs - Pair of Linear Equations in Two Variables

The sum of a two-digit number and the number formed by interchanging its digits is 110. If 10 is subtracted from the first number, the new number is 4 more than 5 times the sum of the digits in the first number. Then, the first number is 64.

A) True

B) False

C) Cannot say

D) Partially true/false

Correct Answer: A

Solution :

Let the digit at units and tens place in the given number be x and y respectively.

Then,

Number\[=\text{ }10y+x\] ... (i)

Number formed by interchanging the digits

\[=10x+y\]

According to the given conditions, we have

\[\left( 10y+x \right)+\left( 10x+y \right)=110\]

and, \[\left( 10y+x \right)-10=5\left( x+y \right)+4\]

\[\Rightarrow \,\,\,\,\,11x+11y=110\]

and, \[4x-5y+14=0\]

\[\Rightarrow \,\,\,\,\,\,\,\,x+y-10=0\] (i)

and, \[4x-5y+14=0\] ...(ii)

On multiplying Eq. (i) by 5, we get

\[5x+5y-50=0\] ...(iii)

On adding Eqs. (ii) and (iii), we get

\[9x-36=0\]

\[\Rightarrow \,\,9x=36\]

\[\Rightarrow \,\,\,x=4\]

From Eq. (i),

\[4+y-10=0\]

\[\Rightarrow \,\,\,\,y-6=0\]

\[\Rightarrow \,\,\,y=6\]

Putting the value of x and y in Eq. (i),

we get

Number \[=10\times 6+4=\text{ }64\]