Question

both question no 18 ,19​

Answer 1

18.

GIVEN :-

Sum of digits of a two digit number is 5.

The number obtained by reversing the digits diminished the orignal no. by 9.

TO FIND :- The Numbers

SOLUTION :-

Let the numbers be x and y.

x + y = 5 ... eq.01

The no. xy can be written as

10x + y

A/Q :- 10x + y - (10y + x ) = 9

=> 10x + y - 10y - x = 9

=> 9x - 9y = 9

=> x - y = 1 ... eq.02

Now, we shall solve both the linear equations in two variable by substitution method.

y = 5 - x ( from eq.01)

=> x - y = 1

=>x - ( 5 - x )= 1

=> x - 5 + x = 1

=> 2x - 5 =1

=> x = 3 (ans)

Substituting this value in eq. 02

x - y = 1

=> 3 - y =1

=> - y = -2

=> y = 2 (ans)

Therefore the numbers are 32 and 23.

19.

GIVEN :-

Let x be the tens digit number.

y be the once/unit digit number.

x = 2y ... eq.01

10x + y -( 10y + x ) = 36

=> 10x + y - 10y - x = 36

=> 9x - 9y = 36

=> x - y = 4 ... eq.02

TO FIND :- The digits

SOLUTION :-

Inorder to find the numbers we shall solve both the linear equations in two variable by substitution method.

x = 2y (from eq. 01)

Putting this value in eq. 02 ,

2y - y = 4

=> y = 4 (Ans)

Substituting this value in eq. 01 ,

x = 2y = 2× 4 = 8

=> x = 8 (Ans)

The numbers are 48 and 84.