Question

e. What did the narrator do in haste so as to not lose the man? the question belongs to chapter face on the wall
​

Answer 1

Answer:

Given that,

The denominator of a fraction is greater than the numerator by 4.

Let assume that

Numerator of a fraction is x

So,

Denominator of a fraction is x + 4.

So, Required fraction is

\begin{gathered}\rm \: Original \: Fraction \: = \: \dfrac{x}{x + 4} \\ \end{gathered}

OriginalFraction=

x+4

x

Now, Further given that

if 11 is added to the numerator and 1 is subtracted from the denominator, the value of the fraction obtained is 7/3.

So,

Numerator = x + 11

Denominator = x + 4 - 1 = x + 3

So,

\begin{gathered}\rm \: Fraction \: = \: \dfrac{x + 11}{x + 3} \\ \end{gathered}

Fraction=

x+3

x+11

Now, According to statement,

\begin{gathered}\rm \: \dfrac{x + 11}{x + 3} = \dfrac{7}{3} \\ \end{gathered}

x+3

x+11

=

3

7

\begin{gathered}\rm \: 7(x + 3) = 3(x + 11) \\ \end{gathered}

7(x+3)=3(x+11)

\begin{gathered}\rm \: 7x + 21 = 3x + 33 \\ \end{gathered}

7x+21=3x+33

\begin{gathered}\rm \: 7x - 3x = 33 - 21\\ \end{gathered}

7x−3x=33−21

\begin{gathered}\rm \: 4x = 12\\ \end{gathered}

4x=12

\begin{gathered}\rm\implies \:x = 3 \\ \end{gathered}

⟹x=3

So,

\begin{gathered}\rm\implies \:\rm \: Original \: Fraction \: = \: \dfrac{3}{3 + 4} = \dfrac{3}{7} \\ \end{gathered}

⟹OriginalFraction=

3+4

3

=

7

3

Verification :-

\begin{gathered}\rm \: Original \: Fraction \: = \: \dfrac{3}{7} \\ \end{gathered}

OriginalFraction=

7

3

It implies, The denominator of a fraction is greater than the numerator by 4.

Now, if 11 is added to the numerator and 1 subtracted from the denominator, then

\begin{gathered}\rm \: Fraction \: = \: \dfrac{3 + 11}{7 - 1} = \dfrac{14}{6} = \dfrac{7}{3} \\ \end{gathered}

Fraction=

7−1

3+11

=

6

14

=

3

7