Question

Find a fraction which becomes ( 1/2 ) when 1 is subtracted from the numerator and 2 is added to the denominator, and the fraction becomes ( 1/3 ) when 7 is subtracted from the numerator and 2 is subtracted from the denominator.

Answer 1

Answer:

Step-by-step explanation:

Let the numerator and denominator be 'x' and 'y' respectively

x-1/y+2=1/2

2x-2=y+2

2x-y=4.... ..(1)

x-7/y-2=1/3

3x-21=y-2

3x-y=19........(2)

Solving both the equation

x=15

putx=15 in equation (1)

2x-y=4

2x15-y=4

30-y=4

-y=4-30

-y=-26

y=26

Answer 2

Given,

• When 1 subtracted from the numerator and  2 is added to the denominator  then the fraction becomes 1/2.
• When 7 is subtracted from the numerator and 2 is subtracted from the denominator then fraction becomes 1/3.

To Find,

• The Fraction

Solution,

⇒Suppose the numerator be x

And suppose the denominator be y

According to the First Case :-

• When 1 subtracted from the numerator and  2 is added to the denominator  then the fraction becomes 1/2.

$\implies \sf{\dfrac{x - 1}{y +2} = \dfrac{1}{2}}$

$\implies \sf{2(x - 1) = 1(y + 2)}$

$\implies \sf{2x - 2 = y + 2}$

$\implies \boxed{\sf{2x - 4 = y}}$

According to the Second Case :-

• When 7 is subtracted from the numerator and 2 is subtracted from the denominator then fraction becomes 1/3.

$\implies \sf{\dfrac{x - 7}{y -2} = \dfrac{1}{3}}$

$\implies \sf{3(x - 7) = 1(y -2)}$

$\implies \sf{3x - 21 = y - 2}$

$\implies \sf{3x - y = 19}$

$\implies \sf{3x - ( 2x - 4 ) = 19}$

(Put the value of y From First Case)

$\implies \sf{3x - 2x + 4 = 19 }$

$\implies \sf{ x = 19 - 4}$

$\implies \boxed{\sf{ x = 15}}$

Now Put the value of x in First Case :-

$\implies \sf{ y = 2x - 4}$

$\implies \sf{ y = 2(15) - 4}$

$\implies \sf{y = 30 - 4}$

$\implies \boxed{\sf{ y = 26}}$

Therefore ,

$\star{\boxed{\sf{\purple{The \ Fraction = \dfrac{15}{26}}}}}$

$\rule{200}2$