Question

if numerator and denominator both are increased by 7 the fraction becomes 5/6. If the numerator is decreased by 2 both the denominator is increased by one fraction becomes 1/6. the sum of the numerator and denominator is​

Answer 1

Answer:

let numerator = x

denominator = y

A.T.Q

x+7/y+7=5/6

6(x+7) = 5(y+7)

6x+42 = 5y+35

6x-5y = 35-42

6x-5y = -5

second eqn =

x-2/y+1=1/6

6x-12 = y+1

6x-y = 13

1eqn + second eqn

6x-5y=-5

6x-y=13

-6y=8

y=-8/6

put y in second eqn

6x-(-8/6)=13

6x+8=78

6x=78-8=70

x=70/6=35/3

y=-8/6

x=35/3

35/3 +(-8/5) = 31/3

Answer 2

$\large\bf\underline{Question:}$

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 fraction becomes 1/6.The sum of the numerator and denominator is?

$\large\bf\underline{Solution:}$

Let the original fraction be x/y.

According to the first condition,

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

According to the second condition,

$\frac{x -2}{y + 1} = \frac{1}{6 } \\ 6x -12 =y + 1 \\ 6x - y = 13---(ii)$

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

$4y= 20 \\ </p><p>y = 5$

Put in equation (ii)

$6x-5=13 \\ </p><p>6x=18 \\ </p><p>x=3$

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

$\implies x + y \\ \implies3 + 5 \\ \implies8$

Hence,the sum of numerator and denominator is 8.

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