Question

A fraction becomes (4/5) if 1 is added to both numerator and denominator if however 5 is subtracted from both numerator and denominator fractions becomes (1/2)what is the fraction ​

Answer 1

Solution :-

Let the numerator and denominator be x and y respectively.

Fraction = x/y

Case I : A fraction becomes 4/5 if 1 is added to both numerator and denominator.

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

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

=> 5x + 5 = 4y + 4

=> 5x - 4y = - 1 ______(i)

Case II : 5 is subtracted from both numerator and denominator fractions becomes 1/2.

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

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

=> 2x - 10 = y - 5

=> y = 2x - 5 _____(ii)

Substituting the value of y in equation (i) we get,

=> 5x - 4(2x - 5) = - 1

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

=> 3x = 21

=> x = 21/3 = 7

Now, In equation (ii),

y = 2 × 7 - 5 = 14 - 5 = 9

Hence,

Fraction = 7/9

Answer 2

Answer :- 7/9

Given :-

The fraction is 4/5 when we add 1 both in numerator and denominator but when we subtract 5 from numerator and denominator the fractions becomes 1/2

To Find :-

The fraction

Solution :-

Let the required fraction be x/y respectively.

According to the first statement we get,

x + 1/y + 1 = 4/5

5x + 5 = 4y + 4

5x + 4y = - 1 ---(1)

According to the second condition we get,

x - 5 / y - 5 = 1/2

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

Multiplying equation (1) by 2 and equation (2) by 5 respectively.

• 5x + 4y = - 1

2( 5x + 4y = - 1)

10x + 8y = - 2 ---(3)

• 2x - y = 5

5(2x - y = 5)

10x - 5y = 25 ---(4)

From equation (3) and (4) We get,

x = 7 and y = 9

Therefore, the required fraction is 7/9.