Question

a fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8 is added to its denominator. the fraction obtained is:
3/5
7/9
5/12
3/8

Answer 1

GIVEN :–

• A fraction becomes 1/3 when 1 is subtracted from the numerator.

• Fraction becomes 1/4 when 8 is added to its denominator.

TO FIND :–

• Fraction = ?

SOLUTION :–

• Let the fraction –

$\\ \rm \implies Fraction = \dfrac{x}{y}$

• According to the first condition –

$\\ \rm \implies \dfrac{x - 1}{y} = \dfrac{1}{3}$

$\\ \rm \implies 3(x - 1) = (1)(y)$

$\\ \rm \implies 3x -3= y$

$\\ \rm \implies y = 3x -3 \: \: \: - - - - eq.(1)$

• According to the second condition –

$\\ \rm \implies \dfrac{x}{y + 8} = \dfrac{1}{4}$

$\\ \rm \implies (4)(x) = (1)(y + 8)$

$\\ \rm \implies 4x=y + 8$

• Now Using eq.(1) –

$\\ \rm \implies 4x=(3x - 3)+ 8$

$\\ \rm \implies 4x=3x - 3+ 8$

$\\ \rm \implies 4x - 3x = - 3+ 8$

$\\ \rm \implies 4x - 3x = 8-3$

$\\ \large\implies { \boxed{ \rm x =5}}$

• Put the value of 'x' in eq.(1) –

$\\ \rm \implies y = 3(5)-3$

$\\\rm\implies y=15-3$

$\\ \large\implies { \boxed{ \rm y=12}}$

• So that –

$\\ \large\implies{ \boxed{ \rm Fraction = \dfrac{5}{12}}}$

• Hence , Third option is correct .

Answer 2

Answer:

✪ Given :-

• A fraction becomes ⅓ when 1 is substracted from the numerator and it becomes ¼ when 8 is added to its denominator.

✪ To Find :-

• What is the fraction.

✪ Solution :-

» Let, the numerator be x

» Let, the denominator be y

» Hence, the fraction will be $\dfrac{x}{y}$

➣ According to the question,

⇒$\dfrac{(x - 1)}{y}$ = $\dfrac{1}{3}$

⇒ y = 3x - 3 ..... Equation no (1)

➵ Again,

⇒$\dfrac{x}{(y + 8)}$ = $\dfrac{1}{4}$

⇒y + 8 = 4x

⇒ y = 4x - 8 ..... Equation no (2)

➣ By solving the equation no (1) and (2) we get,

⇒ 3x - x = 4x - 8

⇒ 3x - 4x = - 8 + 3

⇒ - x = - 5

➠ $\boxed{\bold{\large{x\: =\: 5}}}$

↦From the equation no (1),

⇒y = 15 - 3

➠ $\boxed{\bold{\large{y\: =\: 12}}}$

➙ So, the fraction will be $\dfrac{5}{12}$

$\therefore$ The fraction is $\dfrac{5}{12}$ ✯

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