Question

the denominator of a rational number is greater than its numerator by 8if the number is increased by 17 and the denominator is decreased by 1 the number obtained is 3 /2find the rational number​

Answer 1

Answer:

The rational number is $\bf\dfrac{13}{21}$

Explanation:

Given, Denominator of a fraction 8 more than it's numerator.

If we assume numerator as x

Then, denominator will be (x + 8)

Now,

If numerator increased by 17

• New numerator = (x + 17)

And also, denominator decreased by 1.

• New Denominator = (x + 7)

According to the question,

$\rm \implies \: \dfrac{(x + 17)}{(x + 7)} = \dfrac{3}{2}$

Solving for ‘x’ :-

$\rm \implies \: {2(x + 17)} = {3(x + 7)}$

$\rm \implies \: {2x + 34} = {3x + 21}$

$\rm \implies \: { 34 - 21} = 3x - 2x$

$\rm \implies \: {13} = x$

∴ The value of ‘x’ is 13.

Hence,

• Numerator is = x = 13
• Denominator = (x + 8) = 21

Required fraction: $\bf\dfrac{13}{21}$

Answer 2

Question :-

the denominator of a rational number is greater than its numerator by 8if the number is increased by 17 and the denominator is decreased by 1 the number obtained is 3 /2find the rational number.

Solution :-

the denominator of a rational number is greater than its numerator by 8.

• x + 8

if the number is increased by 17.

• x + 17

the denominator is decreased by 1.

• x + 8 - 1 = x + 7

the number obtained is $\frac{3}{2}$

$\sf: \longmapsto{ \frac{x + 17}{x + 7} = \frac{3}{2} }$

On cross multiply

$\sf: \longmapsto{2(x + 17) = 3(x + 7) } \\ \\ \sf: \longmapsto{2x + 34 = 3x + 21} \: \: \: \\ \\ \sf: \longmapsto{3x - 2x = 34 - 21} \: \: \ \\ \\ \bf: \longmapsto \red{x = 13} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Now,

$\sf: \longmapsto{ \frac{13 + 17}{13 + 7} } \\ \\ \sf: \longmapsto{ \frac{30}{20} } \: \: \: \: \: \: \: \\ \\ \bf: \longmapsto \red{ \frac{3}{2} } \: \: \: \: \: \: \: \:$

Required fraction : $\frac{3}{2}$

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The sum of numerator and denominator of a faction is 13.If 3 is added to numerator and 5 to denominator, the fraction becomes 1/2Find the fraction.

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