Question

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.

Answer 1

Answer :

Let us take the two natural numbers as x and y where x > y

By the given conditions,

x - y = 6

or, x = y + 6 ...(i)

2x + 10 = 3y - 2

or, 2 (y + 6) = 3y - 2, by (i)

or, 2y + 12 = 3y - 2

or, 3y - 2y = 12 + 2

or, y = 14

Putting y = 14 in (i), we get

x = 14 + 6 = 20

Therefore, the two natural numbers are 20 and 14.

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Answer 2

Let the first number be a

Second number = a + 6

According to question,

2 ( a + 6) + 10 = 3a - 2

=> 2a + 12 + 10 = 3a - 2

=> 2a + 22 = 3a - 2

=> 22 + 2 = 3a - 2a

=> a = 24

First number = 24

Second number = 24 +6 = 30