Question

the numerator of a fraction is 3 less than its denominator. If we add 1 to both numerator and denominator it becomes equal to 1/2. Find the fraction

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Answer 1

The fraction is 2/5 .

Solution :-

The numerator of a fraction is 3 less than its denominator.

• n = d – 3

If we add 1 to both numerator and denominator it becomes equal to 1/2 .

• (n+1/d+1) = 1/2

Cross multiply ,

=> 2(n+1) = 1(d+1)

=> 2n + 2 = d + 1 ----------(1)

Replace n with (d-3), from the 1st equation

=> 2(d - 3 ) + 2 = d + 1

=> 2d - 6 + 2 = d + 1

=> 2d - 4 = d + 1

=> 2d - d - 4 = 1

=> d = 5

Put d = 5 in equation (1) ,

=> 2n + 2 = 5 + 1

=> 2n + 2 = 6

=> 2n = 4

=> n = 2

Therefore, 2/5 is the fraction.

Answer 2

$\large\bf\underline \blue {To \: \mathscr{f}ind:-}$

• we need to find the fraction.

$\huge\bf\underline \red{ \mathcal{S}olution:-}$

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

• The numerator of a fraction is 3 less than its denominator.

• If we add 1 to both numerator and denominator it becomes equal to 1/2.

${ \blue{ \mathscr{ \underline{Let : - }}}}$

• Let the numerator be x
• Let the denominator be y

$\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccourding} \: to \: \mathscr {Q} \bf{uestion} ....}}}$

If 1 is added to both numerator and denominator it becomes equal to 1/2.

↛ (x + 1)/(y + 1) = 1/2

↛ 2(x + 1) = y + 1

↛ 2x + 2 = y +1 ....1)

• The numerator of a fraction is 3 less than its denominator
• Numerator x = y - 3 ...2)

• substituting value of x in ...1)

↛ 2(y - 3) + 2 = y + 1

↛ 2y - 6 + 2 = y + 1

↛2y - y - 4 = 1

↛ y = 5

• Substituting value of y in ...2)

↛ x = y - 3

↛ x = 5 - 3

↛ x = 2

Hence,

• Numerator x = 2
• Denominator y = 5

• Fraction x/y = 2/5

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