Question

If numerator and denominator both are increased by 7 the fraction becomes 5/6
if the numerator is decreased by 2 and the denominator is increased by one the fraction becomes 1/6
The sum of numerator and denominator of the fraction is :
A. 8
B. 15
C. 7

Answer 1

Step-by-step explanation:

Let the original fraction be x/y.

According to the first condition,

$\begin{gathered} \frac{x + 7}{y + 7} = \frac{5}{6 } \\ 6x + 42 = 5y + 35 \\ 6x - 5y = - 7 ---(i)\end{gathered}$

$y+7x+7=656x+42=5y+356x−5y=−7−−−(i)$

• According to the second condition,

$\begin{gathered} \frac{x -2}{y + 1} = \frac{1}{6 } \\ 6x -12 =y + 1 \\ 6x - y = 13---(ii)\end{gathered}y+1x−2=616x−12=y+16x−y=13−−−(ii)$

By subtracting equation (i) from (ii),we get,

$\begin{gathered}4y= 20 \\ y = 5\end{gathered}4y=20 \: y=5$

$\tt\large\underline\red{Put \: in \: equation (ii)}$

$\begin{gathered}6x-5=13 \\ /p 6x=18 \\ x=3\end{gathered}6x−5=136x=18</x=3$

• We need to find the sum of the numerator and denominator.

$\begin{gathered} \implies x + y \\ \implies3 + 5 \\ \implies8\end{gathered}⟹x+y⟹3+5⟹8$

Hence,Option (A)s Correct.

• Kindly Scrool Right For Full Sol.

Hope it helps.

Answer 2

Answer:

8

Step-by-step explanation:

let numerator be x and denominator be y

now according to question...

x+7/y+7= 5/6..

6x+42=5y+35

also...

x-2/y+1=1/6

or 6x-12=y+1

now find the value of x by equalising y

We will get x= 3

by using x we find y as 5

finally x+y =8

hope this will help you

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