Question

The sum of two digit number and the number obtained on reversing the digits is 165.If the digits differ by 3,find the numbers? ​

Answer 1

Step-by-step explanation:

Given that:

Sum of 2 digit number and number obtained by reversing is = 165

The digits differ by 3

and also ten’s digit is bigger than unit’s digit

Let the digits of the number be x and y

So by applying the given conditions we get the following equations:

(10x+y)+(10y+x)=165 ————–(i)

x-y=3 ——————-(ii)

11x+11y=165

Taking out 11 as a common factor

x+y=15 ———————-(iii)

Solving (ii) and (iii) we get,

2x=18

x=9

y=15–9=6

Hence the number is 96

Verification:

We can verify by substituting the values in the given conditions:

96 + 69 = 165

9-6=3

Hence both the conditions are verified.

96 is the required number.

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Answer 2

Answer:

96 or 69

Step-by-step explanation:

Let the digits be x and y

Given,

x-y = 3 ---(1) / y-x = 3 ---(2)

and

(10x + y) + (10y + x ) = 165

11x + 11 y = 165

x+ y = 15 ---(3)

Adding (1)&(3) Adding (2) &(3)

we get we get

x= 9 x= 6

y= 6 y= 9

so the number could be either 96 or 69

I hope my explanation will help you with your query