Question

the difference between two positive integers is 50 and the ratio of these integerse 1:3. find these integers​

Answer 1

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

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• Diff. btw 2 positive integers is 50
• Ratio of the integers is 1 : 3

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$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

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• Find the integers = ??

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$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

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let 1st integer be x

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2nd integer = x + 50

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Acc. to the question :-

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$\sf :\implies\:{\dfrac{x}{x+50} = \dfrac{1}{3}}$

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$\sf :\implies\:{3x = x + 50 }$

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$\sf :\implies\:{3x - x = 50}$

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$\sf :\implies\:{2x = 50}$

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$\sf :\implies\:{x = \dfrac{50}{2}}$

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$\sf :\implies\:{x = 25 }$

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• putting value of x in the numbers

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1st number = x = 25

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2nd number = x + 50 = 25 + 50 = 75

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

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• Required positive integers are 25 and 75

Answer 2

$\Large{\underline{\underline{\mathfrak{\red{\bf{Solution}}}}}}$

$\Large{\underline{\mathfrak{\orange{\bf{Given}}}}}$

• the difference between two positive integers is 50
• the ratio of these integerse 1:3

$\Large{\underline{\mathfrak{\orange{\bf{Find}}}}}$

• These Integers

$\Large{\underline{\underline{\mathfrak{\red{\bf{Explanation}}}}}}$.

Let,

• First Integers = x
• Second Integers = y

Case 1.

(the difference between two positive integers is 50)

↪ x - y = 50 ___________(1)

Case 2.

(the ratio of these integerse 1:3)

↪ x : y = 1: 3

↪x/y = 1/3

↪3x - y = 0 _____________(2)

Subtract equ(1) & equ(2)

↪ x - 3x = 50

↪-2x = 50

↪x = -50/2

↪x = -25

Keep Value of x in equ(1)

↪ -25 - y = 50

↪y = -25 - 50

↪y = -75

$\Large{\underline{\mathfrak{\orange{\bf{Since}}}}}$

According to question, both Integers are positive , so Neglect negative sign by all values.

$\Large{\underline{\underline{\mathfrak{\red{\bf{Hence}}}}}}$.

• First Integers will be = 25
• Second Integers will be = 75

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