Question

The sum of numerator and denominator of a proper fraction is 13 and their difference is 3 . Find the fraction
(a) 5/8 (b) 8/5 (c) 3/5 (d) 4/7

Answer 1

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✳ Required Answer:

✏ GiveN:

• The fraction is a proper fraction
• The Sum of numerator and denominator is 13
• The Difference of denominator and numerator is 3

✏ To FinD:

• The fraction...?

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✳ How to solve?

For of all, it is given that the fraction is a proper fraction. It means the denominator of the fraction > numerator of the fraction. So, firstly we have to take numerator and denominator to be any variable to form equation. We will get two equations, one for sum and another one for difference. After that, we can solve it for getting our numerator and denominator.

✒ In this way, we can solve this question.

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✳ Solution:

Let:

• Numerator be x
• Denominator be y

Then, According to question

⏹ Numerator + Denominator = 13

$\large{ \rm{ \longrightarrow \: x + y = 13.........(1)}}$

Then, it is also given

Difference of numerator and denominator is 3 but as it is a proper equation, the denominator is greater than numerator.

⏹ Hence,

Denominator - Numerator = 3

$\large{ \rm{ \longrightarrow \: y - x = 3..........(2)}}$

Adding eq.(1) and eq.(2),

$\large{ \rm{ \longrightarrow \: \cancel{x} + y + y - \cancel{ x }= 13 + 3}} \\ \\ \large{ \rm{ \longrightarrow \:2y = 16}} \\ \\ \large{ \rm{ \longrightarrow \: y = \frac{16}{2} = 8}}$

Putting value of y in eq.(1),

$\large{ \rm{ \longrightarrow \: x + 8 = 13}} \\ \\ \large{ \rm{ \longrightarrow \: x = 5}}$

⏹ Hence,

• The denominator is 8
• Numerator is 5

Our required fraction is:

$\large{ \rm{ans - { \boxed{ \rm{ \red{ \frac{5}{8} }}}}}}$

✏ Option A

$\large{ \therefore{ \underline{ \underline{ \rm{ \purple{Hence \: solved \: \dag}}}}}}$

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Answer 2

Let the numerator and denominator be x and y

then fraction = x/y

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

1. Sum of numerator and denominator is 13.
2. Difference between numerator and denominator is 3.

• ( x + y = 13 -------(1))
• ( x - y = 3 ---------(2))

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

Fraction.

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

$\underbrace{ \bf \: According \: to \: question}$

$\rm \: x + \cancel{y} + x - \cancel{y} = 13 + 3 \\ \\ \implies \rm \: 2x = 16 \\ \\ \implies\: x = 8 \\ \\ \implies \rm \:Putting\:the\:value\:of\:x\:in\:(1) \\ \\ \implies \rm \: 8 + y = 13 \\ \\ \implies \rm \: y = 5$

$\bigstar$ The fraction is $\rm \frac{x}{y}$=$\rm \frac{8}{5}$