Question

If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces to 1 it becomes 1/2 if we add 1 to the denominator. What is the fraction? Plz form an equation and find their solution by elimination method .

Answer 1

$\large\bf\underline {To \: find:-}$

• we need to find the fraction.

$\large\bf\underline{Given:-}$

• If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces to 1 it becomes 1/2 if we add 1 to the denominator.

$\huge\bf\underline{Solution:-}$

• Let the numerator be x
• Let the denominator be y
• Fraction = x/y

❥ According to Question :-

If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces to 1

➛ (x + 1)/(y - 1)= 1

➛ x + 1 = y - 1

➛ x - y = -2 .......1)

If one is added to the denominator the fraction becomes ½

➛ x/y + 1 = ½

➛ 2x = y + 1

➛ 2x - y = 1 .....2)

⏭️ Solving equation 1) and 2)

⠀⠀⠀x ⠀-- ⠀y ⠀= ⠀-2

⠀⠀⠀2x⠀--⠀y = ⠀1

⠀⠀⠀-- ⠀⠀⠀ + ⠀⠀--⠀⠀⠀

⠀⠀⠀- x⠀⠀⠀⠀⠀= -3

• x = 3

⏺️ putting value of x in equation 1)

➛ x - y = -2

➛ 3 - y = -2

➛ - y = -2 - 3

• y = 5

Hence

✝️ The fraction x/y = 3/5

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Answer 2

SOLUTION :-

• If we add 1 to the numerator and subtract 1 from the denominator a fraction reduces to 1

= (x + 1)/(y - 1)= 1

= x + 1 = y - 1

= x - y = -2 .......1)

• If one is added to the denominator the fraction becomes ½

= x/y + 1 = ½

= 2x = y + 1

= 2x - y = 1 .....2)

• Solving equation 1) and 2)

⠀⠀⠀x ⠀-- ⠀y ⠀= ⠀-2

⠀⠀⠀2x⠀--⠀y = ⠀1

_____________

⠀⠀-- ⠀⠀⠀ + ⠀⠀--⠀⠀⠀

⠀⠀⠀- x⠀⠀⠀⠀⠀= -3

x = 3

• putting value of x in equation 1)

= x - y = -2

= 3 - y = -2

= - y = -2 - 3

y = 5

• Hence,

★ The fraction x/y = 3/5