Simple equations STD VI

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?

Answer:

Let the number be y

Therefore the other number is 5y

Also, 2(21 + y) = 5y + 21

Or, 42 + 2y = 5y + 21

Or, 3y = 42 – 21

Or, 3y = 21

Or, y = 7

So, the two numbers are 7 and 35

Sum of the digits of a two-digit number is 9. When we interchange the digits, it is found that the resulting new number is greater than the original number by 27. What is the two-digit number?

Answer:

Let the number in the units place be y

So, the other number is 9-y.

Given, 10(9 – y) + y + 27 = 10y + (9 – y)

Or, 90 – 10y + y + 27 = 10y + 9 – y

Or, 117 – 9y = 9y + 9

Or, 18 y = 117 – 9

Or, y = 108/18 = 6

So, the other number is 9- y = 3

So, the 2 digit number is 36.