Question

If both the numerator and denominator of a fraction
are increased by one, the fraction formed is 2/3. If
both the numerator and denominator are decreased
by two, the fraction formed is 3/5. What is the fraction
formed, if both numerator and denominator are
increased by four?
(A) 7/10 (B) 9/11
(C) 5/7
(D) 3/4​

Answer 1

Answer:

it is called a fraction and answer is d

Answer 2

The correct answer is option (c) 5/7.

Given,

One adding 1 to both numerator and denominator the fraction becomes 2/3 and on decreasing 2 from both the fraction becomes 3/5.

To Find,

The fraction formed when both numerator and denominator are increased by four.

Solution,

Let the numerator and denominator the fraction be x and y respectively.

Now, according to question

(x+1)/(y+1) = 2/3

3(x+1) = 2(y+1)

3x+3 = 2y+2

3x-2y+1 = 0

Now, in seconnd case

(x-2)/(y-2) = 3/5

5(x-2) = 3(y-2)

5x-10 = 3y-6

5x-3y-4 = 0

By solving these linear equations, we get the value of x = 11 and y = 17

Now, the numerator and denominator are increased by 4.

So, the fraction becomes 15/21 = 5/7.

Hence, after increasing the numerator and denominator by 4 the fraction becomes 5/7.