The ratio of two numbers is 2:3. If 2 is substracted from first and 8 from second, the ratio becomes reciprocal of the original ratio. Find the Numbers
Answers
Given That:
The ratio of two numbers is 2:3. 2 is subtracted from first and 8 from second, the ratio becomes reciprocal of the original ratio
We need to find the numbers
Solution
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
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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
Answer:
Given That:
The ratio of two numbers is 2:3. 2 is subtracted from first and 8 from second, the ratio becomes reciprocal of the original ratio
We need to find the numbers
Solution
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
Step-by-step explanation:
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