Question

the difference between two numbers is 8 if 2 is added to the bigger number the result will be 3 times the smaller number find the numbers

Answer 1

Let the first number be a

Second number = a + 8

According to question,

a + 8 + 2 = 3a

=> 10 = 2a

=> a = 5

First number = 5

Second number = a + 8 = 5 + 8 = 13

Answer 2

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✬ Smaller Number = 5 ✬

✬ Larger Number = 13 ✬

Explanation:

Given:

Difference of two numbers is 8.

After adding 2 to bigger number the result will be 3 times the smaller number.

To Find:

What is the number?

Solution: Let the larger and smaller number be x and y respectively. Therefore,

➟ x – y = 8

➟ x = 8 + y.......(i)

A/q

After adding 2 to bigger number the result will be 3 times the smaller number.

${\rm }⟹ x + 2 = 3(y)$

${\rm }⟹ 8 + y + 2 = 3y$

${\rm }⟹ 10 + y = 3y$

${\rm }⟹ 10 = 3y – y$

${\rm }⟹ 10 = 2y$

${\rm }⟹ 10/2 = y$

${\rm }⟹ 5 = y$

So, the two numbers are

➮ Smaller number is y = 5

➮ Larger number is x = 8 + 5 = 13

[ Verification ]

Adding 2 to 13 then we will get result as 3 times of 5.

$\sf{13 + 2 = 3(5)}$

$\sf{15 = 15}$

$\large\bold{\texttt {Verified }}$