the ratio of two no. is 2/3. if 2 is subtracted from the first and 8 from the second...the ratio becomes the reciprocal of the original ratio. find the no.
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Step-by-step explanation:
let the first no be 2x and the second be 3x
if 2 is subtracted from the first no then the equation is
2x-2
if 8 is subtracted from the second no then the equation is
3x-8
and then the ratio becomes 3:2
let 2x-2=3y......(1)
and 3x-8=2y.....(2)
add equation (1) and (2)
(2x-2=3y)+(3x-8=2y)
5x-10=3y
5x-3y=10......(3)
subtract equation (1) from (2)
(3x-8=2y)-(2x-2=3y)
x-6=-y
x+y=-6....(4)
multiply equation (4) by 3
3x+3y=-18....(5)
add equation (3) and (5)
(5x-3y=10)+(3x+3y=-18)
8x=-8
x=-1
first no is 2x=2x-1=-2
second no is 3x=3x-1=-3
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