Question

Find the fraction which becomes 1/2 when the denominator is increased by 4 and is equal to 1/8 when numerator is decreased by 7.

Answer 1

Answer:

13/20

Step-by-step explanation:

lets x/y is the required fraction.

x/y+4 = 1/2

y+4 = 2x

y = 2x - 4 ---------(1)

x-7/y = 1/8

8x - 56 = y ---------(2)

bring both (1) and (2) togrther

8x - 56 = 2x - 4

8x - 2x = 56 - 4

6x = 52

x = 52/6

x = 26/3

substituting the value of x in any equation we can get value of y.

y = 2x - 4

y = 2(26/3) - 4

y = 52/3 - 4

y = 52 / 3 - 12 / 3

y = 40/3

now our required fraction

= x/y

= (26/3) / (40/3)

= 26/40

= 13/20