Question

A two digit number is such that ten's digit exceeds twice the unit by 2 and the number obtained by Interchanging the digits is 5 more than three times the sum of the digits. Find the two digit number​

Answer 1

Answer:

Let the two digit number be 10x+y where y is units digit and x is ten's digit.

It is given that-

x=2y+2 ...(1)

and 10y+x=3(x+y)+5 ....(2)

an solving equation (2) and (1)

10y+x=3x+3y+5

⇒7y−2x=5

∴7y−2(2y+2)=5

3y−4=5

3y=9

y=3

and x=2y+2=6+2=8

the two digit number is 83

Answer 2

Answer:

Let the no: in ten's place be "x'' and that in unit's place be "y". The original no: is 10x + y

Given,

2y + 2 = x  

x - 2y = 2                                  ------> (1)

Also,

No: formed by interchanging the digits is 10y+x

10y + x = 5 + 3(x + y)

10y + x = 5 + 3x + 3y  

2x - 7y = - 5                          -------> (2)

Multiplying equation(1) by 2 :-

2*(x - 2y = 2)

2x - 4y = 4                   -----> (3)

Solving equations (2) and (3),

2x  - 7y = -5

2x - 4y  = 4

-------------------------

-3y = -9

y = 3

x - 2y = 2

x - 6 = 2

x = 2 + 6 = 8

10x + y =  10(8) + 3 = 83

The no: is 83