Question

In a two digit number, the unit's digit is 1 more than twice the ten's digit. If the order of the digit is reversed, the new number is 36 more than the given number. Find the number.

Answer 1

Let the tens place digit be a

Unit place digit = 2a+1

No. = 10(a) + (2a+1)

= 10a+2a+1

= 12a + 1

Reversed no. = 10(2a+1)+ a

= 20a+10 + a

= 21a + 10

According to question

Original no. +36 = Reversed no.

=> 12a+1 + 36 = 21a + 10

=> 21a-12a = 37 - 10

=> 9a = 27

=> a = 3

Unit place digit = 3

Tens place digit = 7

Required no. = 37

Answer 2

Let tens digit be x
Then units digit = 1 + 2x

If order is reversed new number is 36 more.

Sum of digits = 10 (x) + 1 + 2x
= 10x + 1 + 2x

Now reverse
Units digit = x
Tens digit = 1 + 2x

Sum = 10 (1 + 2x) + x = 10 + 20x + x = 10 + 21x

New number - given number = 36

(10 + 21x) - (12x + 1) = 36
9 + 9x = 36
9x = 36 - 9
9x = 27
x = 27/9
x = 3

Tens digit = x
= 3

Units digit = 1 + 2 (3) = 7

Required number = 37

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-ArjunIsCool