Question

When 1 is subtracted from the numerator of a fraction and on simplification, we get 2/3. When 5 is added to the denominator we get 1/2. Find the fraction.​

Answer 1

Answer:

Step-by-step explanation:

Let the numerator and the denominator be x and y respectively.Then,

the required fraction=x/y

Subtracting 1 from numerator and simplifying,the fraction becomes 2/3.Hence,

(x-1)/y=2/3

⇒3(x-1)=2y

⇒3x-3=2y

⇒3x-2y=3 ...(1)

Adding 5 to the denominator and simplifying,the fraction becomes 1/2.Hence,

x/(y+5)=1/2

⇒2x=y+5

⇒2x-y=5 ...(2)

Multiplying eq.(2) by 2, we get

4x-2y=10 ...(3)

Subtracting eq.(1) from eq.(3), we get

x=7

Putting x=7 in eq.(2), we get

2(7)-y=5

⇒14-y=5

⇒y=9

Hence,the required fraction=x/y=7/9