The ratio of two numbers is. If 2 is subtracted from the first and 8 from the second,
the ratio becomes the reciprocal of the original ratio. Find the numbers.
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Let us consider the two numbers as x and y respectively
As per the given ratio
x/y=2/3
3x=2y
3x-2y=0—————-(i)
The second condition
(x-2)/(y-8)=3/2
2x-4=3y-24
2x-3y=-20———————-(ii)
Multiplying equation (i) by 2 and (ii) by 3 we get,
6x-4y=0
– 6x+9y=60
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
On solving these equations we get
5y=60
y=12
Now 3x=2y
x=2y/3 =24/3= 8
So x = 8 and y =12
So the two numbers are 8 and 12
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