Question

The denominator of a rational number is greater than its numerator by 7 if the numerator is increased by 20 and the denominator is decreased by 1, the number obtained is $\frac{5}{3}$ find the rational number. ​

Answer 1

$\huge{\pink{\green {\sf\boxed{ANSWER = \dfrac{15}{22}}}}}$

$\huge{\pink {\sf\underline{Step\: by\: step\: explanation}}}$

Let the numerator be ${x}$

Then, denominator be =${</strong><strong>x</strong><strong> </strong><strong>+</strong><strong> </strong><strong>7</strong><strong>}$

$\Large\boxed{</strong><strong>According</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>to</strong><strong>\</strong><strong>:</strong><strong> </strong><strong>question</strong><strong>⟹</strong><strong> </strong><strong>}$

$</strong><strong>⟹</strong><strong>\</strong><strong>dfrac</strong><strong>{</strong><strong>x</strong><strong> </strong><strong>+</strong><strong> </strong><strong>2</strong><strong>}</strong><strong>{</strong><strong>x</strong><strong> </strong><strong>+</strong><strong> </strong><strong>7</strong><strong> </strong><strong>-</strong><strong> </strong><strong>1</strong><strong>}</strong><strong> </strong><strong>=</strong><strong> </strong><strong>\</strong><strong>dfrac</strong><strong>{</strong><strong>5</strong><strong>}</strong><strong>{</strong><strong>3</strong><strong>}</strong><strong>$

$</strong><strong>⟹</strong><strong> {</strong><strong>3x</strong><strong> </strong><strong>+</strong><strong> </strong><strong>60</strong><strong>}</strong><strong> </strong><strong>=</strong><strong> </strong><strong>{</strong><strong>5x</strong><strong> </strong><strong>+</strong><strong> </strong><strong>35</strong><strong> </strong><strong>-</strong><strong> </strong><strong>5</strong><strong>}$

$⟹ {3x </strong><strong>-</strong><strong> </strong><strong>5x</strong><strong>} = {</strong><strong>35 - </strong><strong>5</strong><strong> </strong><strong>-</strong><strong> </strong><strong>60</strong><strong>}$

$⟹ {</strong><strong>-</strong><strong>2x</strong><strong>} = {</strong><strong>35 - </strong><strong>6</strong><strong>5}$

$⟹ {3x + 60} = {5x + 35 - 5}</strong><strong> </strong><strong>$

$⟹ {</strong><strong>-</strong><strong>2x</strong><strong>} = {</strong><strong>-</strong><strong>30</strong><strong>}$

$⟹ {</strong><strong>x</strong><strong>} = </strong><strong>\</strong><strong>dfrac</strong><strong>{</strong><strong>-</strong><strong>30</strong><strong>}</strong><strong>{</strong><strong>-</strong><strong>2</strong><strong>}</strong><strong>$

$</strong><strong> </strong><strong>\</strong><strong>green</strong><strong> </strong><strong>{</strong><strong>⟹ </strong><strong>{</strong><strong>x</strong><strong>} = {</strong><strong>15</strong><strong>}</strong><strong>}</strong><strong> </strong><strong>$

$\Large\boxed{</strong><strong>Hence</strong><strong>}$

$\small{\pink {\sf\underline{The\: rational\: number ⟹\dfrac{15}{15 + 7}}}}=\small{\pink{\green {\sf\boxed{\dfrac{15}{22}}}}}$

$\huge {\red{\boxed{</strong><strong>Solved</strong><strong>}}}$

#Be_Brainly

Answer 2

$\Large\boxed{Thank \: You..}$