Question

and so
you
2. A positive number is 5 times another number. If 21 is added to both the numbers,
then one of the new numbers becomes twice the other new number. What are the
numbers?
3. Sum of the digits of a two-digit number is 9. When we interchange the digits, it is
27. What​

Answer 1

Answer:

2. Let the another be x

Then, positive no. = 5x

according to your question,

( x + 21 ) × 2 = 5x + 21

or, 2x + 42 = 5x + 21

or, 2x - 5x = 21 - 42

or, - 3x = - 21

or, x = -21/-3

x = 7

Hence, the another no. = x = 7

Therefore positive no. = 5x = 5 × 7 = 35

3. Let the unit place be x

Then, tens place = 9 - x

original no. = 10 (9-x)+x

= 90-10x+x = 90-9x

After interchanging of the digits, the resulting two digit number will be

10x + 9 - x

9x + 9

according to the question,

9x + 9 = 90 - 9x + 27

or, 9x + 9x = 90 + 27 - 9

or, 18x = 108

or, x = 108/18

x = 6

Hence original number = 90 - 9x

= 90 - 9 × 6 = 36.