Question

If 1 is added in the numerator and denominator, then fraction becomes 4 and if we substract 1 from both numerator and denominator then becomes 7 ​, then find the fraction. pls answer urgent

Answer 1

⇝ Given :-

• If 1 is added in the numerator and denominator, then fraction becomes 4

• If we substract 1 from both numerator and denominator then becomes 7.

⇝ To Find :-

• The Original Fraction.

⇝ Solution :-

Let Numerator and Denominator of Original Fraction be :

• Numerator = x

• Denominator = y

So ,

$\text{Original Fraction = } \frac{\text x}{\text y}$

❒ When 1 is added in the numerator and denominator :

$\text{Fraction Becomes : } \frac{\text x +1}{\text y+1}$

⏩ According To Question :

$\frac{\text x + 1}{\text y + 1} = 4$

$:\longmapsto\text x + 1 = 4(\text y + 1)$

$:\longmapsto\text x + 1 = 4\text y + 4$

$:\longmapsto\text x - 4\text y = 4 - 1$

$:\longmapsto \bf x - 4y = 3 \: \: - - - (1)$

❒ When 1 is subtracted from numerator and denominator :

$\text{Fraction Becomes : } \frac{\text x -1}{\text y-1}$

⏩ According To Question :

$\frac{\text x - 1}{\text y - 1} = 7$

$:\longmapsto\text x - 1 = 7(\text y - 1)$

$:\longmapsto\text x - 1 = 7\text y - 7$

$:\longmapsto\text x - 7\text y = -7 + 1$

$:\longmapsto \bf x - 7y = -6 \: \: - - - (2)$

❇ Subtracting (2) from (1) :

$:\longmapsto3\text y = 9$

$:\longmapsto\text y = \cancel\frac{9}{3}$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf y = 3} }}}$

❇ Putting Value of y in (1) :

$:\longmapsto\text x - 4 \times 3 = 3$

$:\longmapsto\text x - 12 = 3$

$:\longmapsto\text x = 3 + 12$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf x = 15} }}}$

Hence,

$\Large\underline{\pink{\underline{\frak{\pmb{Orginal\: Fraction = \frac{15}{3} }}}}}$

Answer 2

Question:

• If 1 is added in the numerator and denominator, then fraction becomes 4 and if we subtract 1 from both numerator and denominator then fraction becomes 7, Find the fraction.

Answer:

• The required fraction is 15/3.

Explanation:

Given that:

• If 1 is added in the numerator and denominator, then fraction becomes 4.
• If we subtract 1 from both numerator and denominator then fraction becomes 7.

To Find:

• The fraction?

Solution:

• Let the numerator of fraction be m and denominator of fraction be n. So, the fraction is numerator/denominator i.e, m/n.

According to the question,

• If 1 is added in the numerator and denominator, then fraction becomes 4.

Therefore,

➻ $\sf \dfrac{m + 1}{n + 1} = 4$

➻ $\sf m + 1 = 4(n + 1)$

➻ $\sf m + 1 = 4n + 4$

➻ $\sf m = 4n + 4 - 1$

➻ $\bf\red{m = 4n + 3}\quad - - - (1)$

Also,

• If we subtract 1 from both numerator and denominator then fraction becomes 7.

Therefore,

➻ $\sf \dfrac{m - 1}{n - 1} = 7$

➻ $\sf m - 1 = 7(n - 1)$

➻ $\sf m - 1 = 7n - 7$

➻ $\sf m = 7n - 7 + 1$

➻ $\bf\purple{m = 7n - 6}\quad - - - (2)$

From (1) and (2) we get,

➻ $\sf 4n + 3 = 7n - 6$

➻ $\sf 7n - 4n = 3 + 6$

➻ $\sf 3n = 9$

➻ $\sf n = {\cancel{\dfrac{9}{3}}}$

➻ $\bf\pink{n = 3}$

Put n = 3 in (2) we get,

➻ $\sf m = (7\:\times\:3) - 6$

➻ $\sf m = 21 - 6$

➻ $\bf\green{m = 15}$

Hence,

✧ Numerator = m = 15

✧ Denominator = n = 3

✧ Fraction = m/n = 15/3

Let's Verify:

We know that,

➻ $\sf \dfrac{m - 1}{n - 1} = 7$

Put m = 15 and n = 3 in above equation we get,

➻ $\sf \dfrac{15 - 1}{3 - 1} = 7$

➻ $\sf {\cancel{\dfrac{14}{2}}} = 7$

➻ $\sf 7 = 7$

➻ $\bf\blue{LHS = RHS}$

Hence, Verified ✔

Learn more on brainly:

Question (1) :-

• The denominator of the rational number is twice the numerator. if the numerator is deceased by 3 and the denominator is increased by 7, the number obtained is 2/7. Find the rational number.

Answer :-

• brainly.in/question/43501561

Question (2) :-

• The denominator of a rational number is less than its numerator than 5.If 5 is added to the numerator, the new number becomes 11/6.Find the original rational number.

Answer :-

• brainly.in/question/43273890

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