Question

16. A fraction becomes 4/5 when 5 is added to its numerator and 1 is subtracted from its denominator. It becomes 1/2 when 3 and 5 are subtracted from its numerator and denominator. The numerator of the fraction will be

(a) 4
(b) 11
(c) 10
(d) 9​

Answer 1

Answer:

b) 11

Step-by-step explanation:

let numerator be x and denominator be y

x+5/y-1 =4/5

5x-4y=-29

&

x-3/y-5=1/2

2x-y=1

y=2x-1

therefore

5x-4(2x-1)=-29

-3x+4=-29

x=11

Answer 2

Step-by-step explanation:

$let \: the \: fraction = \frac{x}{y}$

$\frac{x + 5}{y - 1} = \frac{4}{5}$

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

5x+25=4y-4

5x-4y=-4-25

5x-4y=-29__ (i)

$\frac{x - 3}{y - 5} = \frac{1}{2}$

2(x-3)=1(y-5)

2x-6=y-5

2x-y=-5+6

2x-y=1__(ii)

on solving equation first and second, we get

5x-4y=-29__(i)

2x-y=1___(ii)

on multiply equation first by 1 and equation second by 4, we get

5x-4y=-29

8x-4y=4

- + -

_________

-3x=-33

x=-33/-3

x=11

on putting value of x in equation second, we get

2x-y=1

2×11-y=1

-y=1-22

-y=-21

y=21

hence the fraction =11/21 and numerator of fraction=11