Question

If 1 is added to the numerator of a fraction it becomes ⅓ if 1 is taken from the denominator, it becomes 1/7, find the fraction​

Answer 1

The fraction is 1/9.

Step-by-step explanation:

Given :-

• If 1 is added to the numerator of a fraction, it becomes ⅓.
• If 1 is taken from the denominator, it becomes 1/7.

To find :-

• The fraction.

Solution :-

Let the numerator of the fraction be x and the denominator of the fraction be y.

${\underline{\sf{According\: to\: the\:1st\: condition:-}}}$

• If 1 is added to the numerator of a fraction, it becomes ⅓.

(x+1)/y = ⅓

→ y = 3x + 3...............(i)

${\underline{\sf{According\: to\: the\:2nd\: condition:-}}}$

• If 1 is taken from the denominator, it becomes 1/7.

x/(y-1) = 1/7

→ 7x = y-1

• [ Put y = 3x+3 from eq (i) ]

→ 7x = 3x+3 - 1

→ 7x-3x = 2

→ 4x = 2

→ x = 1/2

• Numerator = ½

Now put x = ½ in eq(I).

y = 3×½ + 3

→ y = 3/2 + 3

→ y = (3+6)/2

→ y = 9/2

• Denominator = 9/2

Therefore,

$\sf{The\: fraction=\dfrac{\dfrac{1}{2}}{\dfrac{9}{2}}=\dfrac{1}{9}}$

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