Question

The difference between two numbers is 8. I f 2 is added to the bigger number the result will be three times the smaller number.find the number

Answer 1

Given

The difference between two numbers is 8. I f 2 is added to the bigger number the result will be three times the smaller number.

Find out

Find the number

Solution

★ Let the numbers be x and y

According to the given condition

✰Difference between two numbers is 8.

• x - y = 8 ----(i)

✰If 2 is added to the bigger number the result will be three times the smaller number.

• x + 2 = 3y
• x = 3y - 2 ----(ii)

Putting the value of x in equation (i)

➟ (x - y) = 8

➟ 3y - 2 - y = 8

➟ 2y - 2 = 8

➟ 2y = 8 + 2

➟ 2y = 10

➟ y = 10/2 = 5

Now put the value of y in equation (ii)

➟ x = (3y - 2)

➟ x = 3 × 5 - 2

➟ x = 15 - 2

➟ x = 13

Hence,

• Required numbers = 5 and 13

$\rule{200}3$

Answer 2

SOLUTION :

$\underline{\bf{Given\::}}}}$

The difference between two number is 8. If 2 is added to the bigger number the result will be three times the smaller number.

$\underline{\bf{To\:find\::}}}}$

The number.

$\underline{\bf{Explanation\::}}}}$

Let the two number be r & m

A/q

$\longrightarrow\sf{r-m=8}\\\\\longrightarrow\sf{r=8+m...................(1)}$

&

$\longrightarrow\sf{r+2=3m}\\\\\longrightarrow\sf{8+m+2=3m\:\:\:[from(1)]}\\\\\longrightarrow\sf{10+m=3m}\\\\\longrightarrow\sf{m-3m=-10}\\\\\longrightarrow\sf{-2m=-10}\\\\\longrightarrow\sf{m=\cancel{-10/-2}}\\\\\longrightarrow\bf{m=5}$

Putting the value of m in equation (1), we get;

$\longrightarrow\sf{r=8+5}\\\\\longrightarrow\bf{r=13}$

Thus;

The two number will 13 & 5 .