Question

Write SOURABH in capital letter and draw each line of symmetry in each letter​

Answer 1

Answer:

Given :

Denominator of a fraction is 3 more than the numerator

The fraction when 2 is added to numerator and 5 is added to denominator is \sf{\dfrac{1}{2}}

2

1

To Find :

The Fraction

Solution :

Let the required fraction be \sf{\dfrac{x}{y}}

y

x

. So that numerator is "x" and denominator is "y"

We are given that denominator of fraction is 3 more than numerator this mean , y = x + 3 ...........(1)

Now numerator and denominator when 2 and 5 are added are , x + 2 and y + 5.

We are given that the fraction when numerator and denominator are added with 2 and 5 as 1/2. So ,

\begin{gathered} \\ : \implies \sf \: \dfrac{x + 2}{y + 5} = \dfrac{1}{2} \\ \\ \end{gathered}

:⟹

y+5

x+2

=

2

1

From eq(1) ,

\begin{gathered} \\ : \implies \sf \: \dfrac{x + 2}{x + 3 + 5} = \dfrac{1}{2} \\ \\ \end{gathered}

:⟹

x+3+5

x+2

=

2

1

\begin{gathered} \\ : \implies \sf \: \dfrac{x + 2}{x + 8} = \dfrac{1}{2} \\ \\ \end{gathered}

:⟹

x+8

x+2

=

2

1

\begin{gathered} \\ : \implies \sf \: 2(x + 2) = 1(x + 8) \\ \\ \end{gathered}

:⟹2(x+2)=1(x+8)

\begin{gathered} \\ : \implies \sf \: 2x + 4 = x + 8 \\ \\ \end{gathered}

:⟹2x+4=x+8

\begin{gathered} \\ : \implies \sf \: 2x - x = 8 - 4 \\ \\ \end{gathered}

:⟹2x−x=8−4

\begin{gathered} \\ : \implies {\underline{\boxed{\pink{ \mathfrak{x = 4}}}}} \: \bigstar \\ \\ \end{gathered}

:⟹

x=4

★

Now , From eq(1) ;

\begin{gathered} \\ : \implies \sf \: y = 4 + 3 \\ \\ \end{gathered}

:⟹y=4+3

\begin{gathered} \\ : \implies{\underline{\boxed{\pink{\mathfrak{y = 7}}}}} \: \bigstar \\ \\ \end{gathered}

:⟹

y=7

★

Now the fraction is \sf{\dfrac{x}{y}}

y

x

= \sf{\dfrac{4}{7}}

7

4

Hence ,

The required fraction is \sf{\dfrac{4}{7}}

7

4