Question

The difference between two numbers is 8. If 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.
• If 2 is added to the bigger number , the result will be 3 times the smaller number.

To find :

• The numbers.

Solution :

Consider,

• Bigger number = x
• Smaller number = y

${\underline{\sf{According\: to\:the\:1st\: condition:-}}}$

• The difference between two numbers is 8.

$\to\sf{x-y=8}$

$\to\sf{x=8+y.................(i)}$

${\underline{\sf{According\: to\:the\:2nd\: condition:-}}}$

• If 2 is added to the bigger number , the result will be 3 times the smaller number.

$\to\sf{x+2=3y}$

$\to\sf{8+y+2=3y\:[put\:x=8+y]}$

$\to\sf{y+10=3y}$

$\to\sf{y-3y=-10}$

$\to\sf{-2y=-10}$

$\to\sf{y=5}$

• Smaller number = 5

Now , put y = 5 in eq(1).

$\to\sf{x=8+y}$

$\to\sf{x=8+5}$

$\to\sf{x=13}$

• Bigger number = 13

Answer 2

$\bigstar{ \large{\sf{ \underline{ \underline{AnSwer:}}}}}$

It is given that the difference between 2 numbers is 8. So,

Let us consider bigger number be x and smaller number be y.

Difference is 8.

So, the equation obtained is,

$\sf \: x-y = 8 - - - \{ 1\}$

Now, if 2 is added to the bigger number the result will be three times the smaller number,

$\sf \: x + 2 = 3y \\ \sf \: x - 3y = -2y - - - \{2\}$

On substracting eqn (2) from (1),

$\sf \longmapsto \: \: x - y - (x - 3y) = 8 - (-2) \\ \\ \sf \longmapsto \: \: x - y - x + 3y = 8 + 2 \\ \\ \sf \longmapsto \: \: 2y = 10 \\ \\ \sf \longmapsto \: \:y = \dfrac{ \cancel10}{ \cancel2} \\ \\ \sf \longmapsto \: \: {\underline{ \boxed {\sf{ \purple{y = 5}}}}} \: \bigstar$

Now, consider the eqn (1),

$\sf \longmapsto \: \: \: x - y = 8 \\ \\ \sf \longmapsto \: \: \: x-5 = 8 \\ \\ \sf \longmapsto \: \: \: x=8+5 \\ \\ \sf \longmapsto \: \: \:{ \underline{ \boxed{ \sf{ \red{x=13}}}}} \: \bigstar$

Therefore, bigger number is 13 while smaller number is 5.