TWO NUMBERS ARE IN THE RATIO 3:5.IF 8 IS ADDED TO EACH NUMBER , THE RATIO BECOMES 2:3. FIND THE 2 NUMBERS.

Let the 2 numbers be 3x and 5x.
3x+8   = 2
 5x+8     3
        
3(3x+8) = 2(5x+8)
9x+24 = 10x+16
x = 8
The 2 numbers are 24 and 40

 

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THE NUMBERS ARE
3:5 = 3/5.
LET COMMON RATIO BE x. THEREFORE, 3 = 3x AND 5 = 5x.
ON ADDING 8 TO BOTH NUMBERS,
(3x+8)/(5x+8)= 2/3. (AS THE RATIO BECOMES 2:3 AFTER ADDING 8 TO BOTH NUMBERS).
BY CROSS MULTIPLICATION,
(3x+8)X(3) = (5x+8) X (2).
9x+24 = 10x + 16.
24-16 = 10x - 9x.
x = 8.
THEREFORE,
3x= 3 X 8 = 24
AND, 5x = 5 X 8 = 40.
SO, THE NUMBER IS 24/40.
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let the numbers be 3x and 5x. when 5 is added to both the numbers, the numbers become 2x and 3x.

so, 3x + 5 + 5x + 5 = 2x + 3x
8x + 10 = 5x
8x - 5x = - 10
3x = - 10
x = -10/3

so, the numbers are:- 2x = -20/3 and 3x = -10
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