Question

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

Answer 1

${\huge {\underline {\sf {Answer}}}}$

Given :-

• The difference between two numbers is 8.

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

To Find :-

• The number.

Solution :-

$\implies$ Let, the bigger number be "x"

$\implies$and the smaller number be "y".

According to the question,

$\implies$${\sf {x-y=8}}$     -----------------  eq. ( i )

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

$\implies$${\sf {x + 2 = 3y}}$        ----------------------   eq. ( ii )

By Substitution method,

From eq. ( i ), we get

$\implies$${\sf {x = 8 + y}}$     ---------------- eq. ( iii )

Substitute the value of "x" from eq. ( iii ) to eq. ( ii )

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

$\implies$${\sf {8 + y + 2 = 3y}}$

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

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

$\implies$${\sf {10 = 2y}}$

$\implies$${\sf {\dfrac {{\cancel{{10}}^{5}}}{{\cancel{2}}}} = y}$

$\implies$${\underline {\boxed {\sf {y = 5}}}}$

Now, substitute the value of "y" in eq. ( iii )

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

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

$\implies$${\underline {\boxed {\sf {x = 13}}}}$

${\sf {\underline {\purple {Hence,~ larger~ number~ is~ 13}}}}$

${\sf {\underline {\purple {and~ the~ smaller~ number~ is~ 5}}}}$

Answer 2

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

To Find : Find the numbers ?

_________________________

Solution : Let the numbers be x and y.

$~$

$\pmb{\sf{\underline{According ~to~ the~ Given Question~:}}}$

$~$

•Difference between two numbers is 8.

$~$

• ${\sf{x ~-~ y ~= ~8\qquad\qquad\bigg\lgroup{Eqⁿ~1}\bigg\rgroup}}$

$~$

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

• ${\sf{x ~+ ~2 ~= ~3y}}$
• ${\sf{x ~=~ 3y ~- ~2\qquad\qquad\bigg\lgroup{Eqⁿ~2}\bigg\rgroup}}$

$~$

◗Putting the values of x in equation 1

$\qquad\qquad{\sf:\implies{\bigg(x~ -~ y\bigg)~ = ~8}}$

$\qquad\qquad{\sf:\implies{3y ~- ~2 ~- ~y ~= ~8}}$

$\qquad\qquad{\sf:\implies{2y ~-~ 2 ~= ~8}}$

$\qquad\qquad{\sf:\implies{2y~ = ~8~ + ~2}}$

$\qquad\qquad{\sf:\implies{2y~ = ~10}}$

$\qquad\qquad{\sf:\implies{y ~=~ \cancel\dfrac{10}{2}}}$

$\qquad\qquad:\implies{\underline{\boxed{\frak{\purple{y~=~5}}}}}$★

$~$

◗Now, Putting the values of y in equation 2

$\qquad\qquad{\sf:\implies{x ~= ~\bigg(3y~ - ~2\bigg)}}$

$\qquad\qquad{\sf:\implies{x~ = ~3~ ×~ 5~ - 2}}$

$\qquad\qquad{\sf:\implies{x ~=~ 15~ - ~2}}$

$\qquad\qquad:\implies{\underline{\boxed{\frak{\pink{x ~= ~13}}}}}$★

$~$

Hence,

$\therefore\underline{\sf{Required ~numbers~is~\bf{\underline{5 ~\&~3}}}}$