Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :- A two digit number is obtained by either multiplying the sum of the digits by 8 and adding 1, or by multiplying the difference of the digits by 13 and adding 2. Find the number.

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :-A number consisting of two-digits, is equal to 7 times the sum of its digits. When 27 is subtracted from the number, the digits interchange their places. Find the number

From the pair of linear equations in the following problems and find their solutions (if they exist) by elimination method : Seven times a given two digit number is equal to four times the number obtained by interchanging the digits and the difference of digits is 3. Find the number

From the pair of linear equations in the following problems and find their solutions (if they exist) by elimination method : A certain number of two digits is three times the sum of its digits and if 45 be added to i,t the digits will be reversed. Find the number.

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :-The sum of a two-digit number and the number formed by interchanging the 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. Find the number

Form the pair of linear equations In the following problems and find their solutions (if they exist) by any algebraic method. :- A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. Find the fraction.

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :- for which value of k the following linear pair of equations have no solution ? 3x + y=1 and (2k-1)x+(k- 1)y= 2k+1.

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :-The sum of numerator and denominator of a fraction is 4 more than twice the numerator. If' the numerator and denominator are increased by 3, they are in the ratio 2:3. Find the fraction.

Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method :- The area of a rectangle is reduced by 9 sq. metres if its length is reduced by 5 metres and the breadth is increased by 3 metres. If we increase the length by 3 units and the breadth by 2 units, area increases by 67 square units. Find the length and breadth of the rectangle.

Form the pair of linear equations In the following problems and find their solutions (if they exist) by any algebraic method. :- The area of a rectangle gets reduced by 9 square units if its length is reduced by 5 units and breadth is increased by 3 units. If we increase the length by 3 units and the breadth by 2 units, the area increases by 67 units. Find the dimensions of the rectangle.