Question

If 1 is subtracted from the numerator and from denominator of a fraction the value obatained 3/4 if 1 is added to its numerator and its denominator the resulting value is 4/5 Find the friction​

Answer 1

Answer:

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Given:

• If 1 is subtracted from the numerator and from the denominator of a fraction, the value obtained is 1/2. If 1 is added to its numerator and to its denominator, the resulting value is 2/3.

To find:

• Find the fraction.

Solution:

Let the fraction be x/y, then:

According to the first statement, we get:

➙ x-1/y-1 = 1/2

Solving this, we get:

➙ 2(x-1) = y-1

➙ 2x - 2 = y - 1

➙ 2x - y - 1 = 0 ______(i)

According to the second statement, we get:

➙ x+1/y+1 = 2/3

Solving this, we get:

➙ 3(x+1) = 2(y+1)

➙ 3x + 3 = 2y + 2

➙ 3x - 2y + 1 = 0 _______(ii)

Now solving: 2(i) - (ii), we get:

➙ 4x - 2y - 2 = 0

➙ - 3x + 2y - 1 = 0

➙ x - 3 = 0

➙ x = 3

Putting x in (i), we get:

➙ 2(3) - y - 1 = 0

➙ 6 - y - 1 = 0

➙ y = 5

Hence, the fraction is :

➙ x/y = 3/5

Henceforth, the fraction is 3/5.