Two numbers are such that the ratio between them is 3:5.If each increased by 5,the ratio between the new numbers so formed is 2:3.Find the original numbers.
Answers
Answer:
The original numbers are 15 and 25
and their ratio = 3:5
= 15:25
Step-by-step explanation:
To find the original numbers
Step 1 = Let the two numbers be 3x and 5x respectively
That is 3x:5x or 3x/5x(ratio actually means division)
Follow the conditions given in the question
That is each increased by 5 and the ratio between the new numbers so formed is 2:3 or 2/3
So now the numbers formed like this -
3x + 5/5x + 5
Step 2 = Now equate the ratios with their results
That is,
3x + 5/5x + 5 = 2/3
3(3x + 5) = 2(5x + 5)[Through cross multiplication]
9x + 15 = 10x + 10
Now take the like terms to one side by changing their signs
9x - 10x = 10 - 15
-x = -5
cut the common sign(negative)
x = 5
The original numbers are
= 3x = 3 X 5(x = 5) = 15
= 5x = 5 X 5(x = 5) = 25
Their ratio is 3:5 = 3x:5x = 15:25