Question

one number is three times another number if 15 is added to both the number then one of the new number becomes twice that of the other new number. find the number​

Answer 1

${\huge {\bf {\underline {\blue {Answer}}}}}$

Solution :-

Let, the number be "x"

other number be "3x"

If "15" is added to both the numbers,

1st number = x + 15

2nd number = 3x + 15

One of the new number becomes twice that of the other new number = 2(x + 15)

According to the question,

$\longmapsto {\sf {3x + 15 = 2(x + 15)}}$

$\longmapsto {\sf {3x + 15 = 2x + 30}}$

$\longmapsto {\sf {3x - 2x = 30 - 15}}$

${\red \longmapsto {\red {\sf {x = 15}}}}$

Therefore,

${\bf {1st~ number = x = 15}}$

${\bf {2nd~ number = 3x = 3 \times x = 3 \times 15 = 45}}$

V E R I F I C A T I O N :-

For verification, put the value of "x" in the eq. " 3x + 15 = 2(x + 15) "

$\longmapsto {\sf {3x + 15 = 2(x + 15)}}$

$\longmapsto {\sf {3 \times 15 + 15 = 2 (15 + 15)}}$

$\longmapsto {\sf {45 + 15 = 30 + 30}}$

$\longmapsto {\sf {60 = 60}}$

$\longmapsto {\sf {LHS = RHS ~}}$

Hence, Verified ✔

Answer 2

Given : When 15 is added to both the numbers, then one of the new numbers become twice that of the other new number.

One Number = Thrice the another.

To Find : Find the numbers ?

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Solution : One number is x and second number is y.

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

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• ${\sf{x~=~3y~~~~~~~~~~\qquad\qquad\qquad\qquad\qquad\bigg\lgroup{Eqⁿ~1}\bigg\rgroup}}$

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As Given : 15 is added to both Numbers by which it becomes,

• ${\sf{x ~+~ 15 ~\&~ y ~+ ~15}}$

• ${\sf{\bigg(x ~+ ~15\bigg)~ =~ 2\bigg(y~ +~ 15\bigg)\qquad\qquad\bigg\lgroup{Eqⁿ~2}\bigg\rgroup}}$

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Now, we have,

• ${\sf{x ~= ~3y~~~~~~~~~ ~~~~~~~~\qquad\qquad\qquad\qquad\bigg\lgroup{Eqⁿ~1}\bigg\rgroup}}$
• ${\sf{\bigg(x ~+ ~15\bigg)~ = ~2\bigg(y~ + ~15\bigg)\qquad\qquad\bigg\lgroup{Eqⁿ~2}\bigg\rgroup}}$

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◗Putting the values of equation 1 & equation 2,

• ${\sf{\bigg(x~ + ~15\bigg)~ =~ 2\bigg(y ~+ ~15\bigg)}}$

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•Using the value of x here,

• ${\sf{\bigg(3y~ + ~15\bigg) ~= ~2\bigg(y~ + ~15\bigg)}}$
• ${\sf{3y ~+~ 15~ = ~2y ~+ ~30}}$

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•Subtraction of 15 from both sides,

• ${\sf{3y ~+~ 15~ -15~ =~ 2y ~+ ~30 ~-15}}$
• ${\sf{3y ~=~ 2y ~+ ~15}}$

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•Subtraction of 2y from both sides,

• ${\sf{3y ~-~ 2y~ = ~2y ~+ ~15 ~-2y}}$
• ${\sf{y~ = ~15}}$

∴ The value of y = 15.

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◗Putting value of y in equation 1,

• ${\sf{x ~= ~3\bigg(15\bigg)}}$
• ${\sf{x ~= ~45}}$

Therefore,

• The value of y = 15 and value of x = 45

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Hence,

$\therefore\underline{\sf{The~ two ~Numbers ~are ~\bf{\underline{45}}~\sf{ \&}~\bf{\underline{ 15}}}}$