Question

two numbers are in ratio 3:5 if 9 is subtracted from each ratio becomes 12:25, find the number

Answer 1

Let us take the given ratio be 3x:5x.

By Subtracting 9 from each the ratio becomes 3x - 9 :3x - 5 .

But it is given 12:25.

So,

ATQ, 3x - 9 :5x - 9 = 12:25

or 3x- 9 / 5x - 9 = 12 / 25.

or 25(3x - 9) = 12(5x - 9)

[BY CROSS MULTIPLYING]

=75x - 225 = 60x - 108.

or 75x - 60x = 225 - 108.

or 15x = 117.

THEREFORE x = 117/15.= 39/5.

Therefore 1st no. = 3x = 3 × 39/5 = 108/5.

Therefore 2nd no. = 5x = 5 × 39/ 5 = 39.

Answer 2

let one no. be x

let another no. be y

then

x/y=3/5. ( this is the 1 St equation)

9 subtracted from each no.

x-9/y-9=12/25. ( this is 2 nd equation)

solve 1 and 2 equations

x/y=3/5

5x=3y first equation

(x-9)25 =(y-9)12

25x-225=12y-108

25x-12y=225-108=117 second equation

now solve both the equations

5x-3y=0 multiply the whole equation 4

25x-12y=117

(-). (+)

20x -12y=0

-25x+12y=-117

-5x +0 =-117

x =117/5

substitute x in equation 1

5(117/5)-3y=0

117-3y=0

117=3y

y=117/3

y=39

now two no.s are. x=117/5,,y=39

x/y =117/5/39

x/y=117/5*39

x/y=117/195

simplified x/y=39/65=3/5