Question

The sum of two no is 8 if their sum is four times there difference find the number?

Answer 1

Let the no's be x and y
A. To. Q
x+y=8--------------------(1)
x+y=4(x-y)
x+y=4x-4y
-3x+5y=0-----------------(2)
3eq(1)+eq(2)
3x+3y-3x+5y=24
8y=23
y=3
So x=5

Answer 2

$\Large{\textbf{\underline{\underline{According\:to\:the\:Question}}}}$

Assumption

$\textbf{\underline{Two\;numbers\;be\;p\;and\;c}}$

Hence,

p + c = 8 …… (1)

Given,

$\textbf{\underline{Sum\;is\;four\;times\;their\; difference.}}$

Therefore,

p + c = 4 (p - c)

8 = 4 (p - c)

$\tt{\rightarrow (p-c)=\dfrac{8}{4}}$

p - c = 2 …… (2)

$\textbf{\underline{Adding\;(1)\;and\;(2)\;we\;get :- }}$

p + c + p - c = 8 + 2

2p = 10

$\tt{\rightarrow p=\dfrac{10}{2}}$

p = 5 …… (3)

${\boxed{\sf\:{Substitute\;the\;value\;of\;(3)\;in\;(1)}}}$

p + c = 8

5 + c = 8

c = 8 - 5

c = 3

$\textbf{\underline{Therefore}}$

$\Large{\boxed{\sf\:{Two\;numbers\;are\;5\;and\;3}}}$