Question

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

Answer 1

Let the biggest number be x

And,

Let the smaller number be y.

Then,

x - y = 8 - - - - - - - - - - (1)

x + 2 = 3y- - - - - - - - - (2)

By substitution method:

x=8+y  [from 1]- - - - - - - - - (3)

Putting the value of (1) in (2)

8+y+2=3y

10=3y-y

10=2y

y=10/2=5

Putting the value of y in (3)

x=5+4

x=13.

Largest no. =13

Smallest no. =5

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.

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

$\sf{15 = 15}$

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