Question

if the numerator and denominator of a certain fraction are each decreased by 2, the value of the new fraction is 1/2. but if the numerator of the original fraction is increased by 1 and the denominator decreased by 2, the resulting fraction is equal to 3/4. find the original fraction.

Answer 1

$\bf\underline{\underline{\blue{SOLUTION:-}}}$

Question

• if the numerator and denominator of a certain fraction are each decreased by 2, the value of the new fraction is 1/2. but if the numerator of the original fraction is increased by 1 and the denominator decreased by 2, the resulting fraction is equal to 3/4. find the original fraction?

Answer

• Original fraction is 8/14

To Calculate

• Original fraction?

Step by step explanation

Let the original fraction be x/y

Case 1

$= \frac{x - 2}{y - 2} = \frac{1}{2}$

➺ 2(x-2)= y-2

➺ 2x-4 = y-2

➺ 2x -y = -2+4

➺ 2x -y = 2 ________(1)

Case 2

$= \frac{x + 1}{y - 2} = \frac{3}{4}$

➺ 4(x+1)=3(y-2)

➺ 4x+4 = 3y-6

➺ 4x-3y = -6-4

➺ 4x-3y = -10 _______(2)

On multiply equation 1 by 2

2(2x-y=2)

➺ 4x-2y=4__________(3)

On Subtracting eq3 from 2

4x - 3y = -10

4x - 2y = 4

_________

y = 14

Putting value of y in eq 3

4x-2y=4

➺ 4x-2×14 =4

➺ 4x-28=4

➺ 4x=4+28

➺ 4x= 32

➺ x= 32/4

➺ x = 8

$\bf\underline{\underline{\blue{HENCE:-}}}$

• Original fraction is 8/14

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Answer 2

Step-by-step explanation:

8/14..... Orignal fraction