Question

A two digit number is obtained by either multiplying sum of the degits by 8 and adding 1 or by multiplying the difference of the digits by 13 and adding two. The number is

Answer 1

EXPLANATION

Let the digit at tens place be x

Let the digit at unit place be y

Then number = 10x + y

IN CASE 1

GIVEN

Two digit number is obtaining by either

multiplying sum of the digit by 8 and

adding 1

The equation will be written as

10x + y = 8 ( x + y) +1

10x + y = 8x + 8y + 1

2x - 7y = 1 .....(1)

IN CASE 2

GIVEN

Multiplying the difference of the digit by 13

and adding 2

The equation will be written as

10x + y = 13 ( x - y) + 2

10x + y = 13x - 13y + 2

-3x + 14y = 2

from equation(1) and equation(2)

we get,

x = 4 and y = 1

the number be

10x + y =

10(4) + 1 = 41 = ANSWER