Math, asked by faithprapty, 16 days ago

If I is added to the numerator and to the denominator of a fraction, the value obtained
Is 4/5. If 5 is subtracted from its numerator and from its denominator, the resulting
value is 1/2. Find the fraction.

Answers

Answered by BrainlyYuVa
6

Solution

Given :-

  • If I is added to the numerator and to the denominator of a fraction,
  • If 5 is subtracted from its numerator and from its denominator, the resulting value is 1/2.

Find :-

  • These Fraction.

Explanation

Let,

  • Numerator be = x
  • Denominator be = y.

According to question,

Case 1.

==> (x+1)/(y+1) = 4/5

==> 5×(x+1) = 4×(y+1)

==> 5x - 4y = 4 - 5

==> 5x - 4y = -1_________(1)

Again,

==> (x-5)/(y-5) = 1/2

==> 2×(x-5) = (y-5)

==> 2x - y = -5 + 10

==> 2x - y = 5__________(2)

Multiply by 4 in equ(2)

==> 8x - 4y = 20________(3)

Sub. equ(1) & equ(3)

==> 5x - 8x = -1 - 20

==> -3x = -21

==> x = 21/3

==> x = 7 .

Keep in equ(1)

==> 5×7 - 4×y = -1

==> 4y = 35 + 1

==> 4y = 36

==> y = 36/4

==> y = 9

Hence

  • Numerator will be = 7
  • Dominator will be = 9

Since

Required Fraction.

  • Fraction will be (x/y) = 7/9 .

____________________

Answered by rishabhshah2609
0

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

                   x/y = 3/5

Answer:

               So the fraction is 3/5.

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