Q6 of 71 Page 68

The difference between two natural numbers is 6. Adding 10 to the twice of the larger number, we get 2 less than 3 times of the smaller number. Find these numbers.

Let the two natural numbers be x and y such that x is the larger number and y is the smaller number.


According to the question,


x – y = 6


and 2x + 10 = 3y – 2


⇒ x – y – 6 = 0 …(i)


And 2x – 3y + 12 = 0 ..(ii)


Multiply (i) by 2,


2x – 2y – 12 = 0 .. (iii)


2x – 3y + 12 = 0 ..(ii)


Subtract (iii) from (ii),


2x – 3y + 12 – 2x + 2y + 12 = 0


⇒ – y + 24 = 0


⇒ y = 24


Putting this value in (i),


x – 24 – 6 = 0


⇒ x = 30


So the numbers are 30 and 24.


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