Question

Sum of the digits of 2 digit number multiplied by 8 and 1 added to it gives the two digit number also the difference of the digits multipied by 13 and then 2 added to it it also gives the same two digit number find the number

Answer 1

Answer:

..

Step-by-step explanation:

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Answer 2

Answer:

THE 2-DIGIT NUMBER IS  41

Step-by-step explanation:

Let the digit at the units place by x and at ten's place be y

∴ The required number = 10y + x

ACCORDING TO THE FIRST CONDITION-

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

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

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

1 = 2y - 7x :::::::::::::: equation (1)

ACCORDING TO THE SECOND CONDITION-

difference of the digits = either x-y or y-x

∴ 13(y-x) + 2 =  10y + x

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

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

2 = 14x - 3y  :::::::::::::: equation (2)

NOW MULTIPLY (1) BY 2

1 x 2 = 2y x 2 - 7x x 2

2 =  4y - 14x     :::::::::::::: equation (3)

SOLVE (2) AND (3) SIMULTANEOUSLY

ADD:-

2 = 14x - 3y

2 = -14x + 4y :::::::::::::: (14 - 14 gets cancelled)

y = 4

SUBSTITUITING

1 =  2y - 7x

1 = 2(4) - 7x

1 = 8 - 7x

7x = 8 - 1

7x = 7

x = 1

THE NUMBER IS 10y + x

SUBSTITUITING

10(4) + 1

40 + 1

41