Question

A fraction becomes 3/5 if 1 is added to both numerator and denominator.if,however,3is subtracted from the both numerator and denominator the fraction becomes 1/3.what is the fraction?

Answer 1

Answer:

Let fraction be

y

x

According to question, we have

y+1

x+1

=

5

4

⇒5x+5=4y+4

⇒5x−4y=−1 .(i)

Again

y−5

x−5

=2

⇒2x−10=y−5

⇒2x−y=5 .(ii)

Multiplying equation (ii) by 4

8x−4y=20

and then subtracting from (i), we get

−3x=−21

⇒x=7

Putting x=7 in (i), we get

5×7−4y=−1

⇒35+1=4y⇒y=

4

36

=9

Hence, required fraction is

9

7

Answer 2

Answer:

Let the fraction be

y

x

.

According to question,

x-5/y-3=1/2

⇒2(x−5)=y−3

⇒2x−10=y−3

⇒2x−y=7...(1)

and y=5+x

⇒−x+y=5...(2)

Adding equation 1 and 2 we get,

2x−y−x+y=7+5⇒x=12

Putting value of x in equation 2 we have,

−12+y=5⇒y=5+12=17

Thus, the fraction becomes,

12/17

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