Question

given rational number. Find 7. Sum of the digits of a 2-digit number is 8. When the digits of the number are interchanged, the resultin new number is smaller than the original number by 36. What is the original number?​

Answer 1

Answer:

62

Step-by-step explanation:

Let digits of number be x and y

So number = 10x+y

Sum of digits =8=x+y______EQ1

Digits interchanged, so new number = 10y+x

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

10x+y-10y-x=36

9x-9y=36

x-y=4______EQ2

From EQ1 and EQ2,

x= 6 and y = 2

so number = 10x+y=10*6+2=60+2=62

Answer 2

Maybe you are tying to ask: Sum of the digits of a 2-digit number is 8. When the digits of the number are interchanged, the resulting new number is smaller than the original number by 36. What is the original number?​

Step-by-step explanation: For such questions we generally take an unknown variable and then use concept of place values to find the sum of the digits and then find the actual number.

Now lets see how to proceed :

Let the one's digit of the two digit number be x and the ten's digit be 8-x.

(How? well, its given that sum of the two digits of the number is 8, so if one is x other is 8-x)

So, original number :

=> x + 10(8-x)

=>  80-9x                            -------------------(i)

Now a/c to the conditions given in question->

(1) On interchanging the digits : Now ones digit will be 8-x and tens digit will be x.

So the new number is:

=>  8-x + 10x

=>  8+9x                          ----------------------(ii)

(2) On combining the equation (i) and (ii) with the condition given in question we get->

=>8+9x + 36 = 80-9x

=>18x = 36

=> x = 2

Hence, on putting back value of x in equation (i) we get the original number as 80-(9×2) =62.