1.

2. The digits of a two-digit number differ by 3. If the digits are interchanged, and the resulting number is addedto the original number, we get 143. What can be the original number?

Answer»

Answer:

58

Step-by-step explanation:

let the digits be x. and y

and number be 10y + x

given that,

The digits of a two-digit number differ by 3

so,

x - y = 3 ......(1)

now ,

also given that,

If the digits are interchanged,

and the resulting number is added to the original number,

we get 143.

original number = 10y + x

interchanged number = 10X + y

so,

ATQ,

10y + x + 10x + y = 143

11x + 11y = 143

11(x + y) = 143

x + y = 143/11

x + y = 13 ...(2)

now,

adding (1) and (2)

(1) + (2)

x - y + x + y = 3 +13

2x = 16

x = 16/2

x = 8

now,

putting the value of x on (1)

x - y = 3

8 - y = 3

-y = 3 - 8

-y = -5

y = 5

original number = 10y + x

10(5) + 8

50 + 8

58

so,

original number = 58


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