the ratio between two natural numbers is 3:5 find the smallest number

Question

the ratio between two natural numbers is 3:5 find the smallest number which must be added to these numbers so that the resultant numbers are in ratio of 9:14

Answer 1

3:5 and 9:14 is akin to 3/5 and 9/14 respectively. So if we were to set up a math problem, it would look like this:

3/5 + a = 9/14

 

We need to get a alone, so we subtract 3/5 to both sides:

a = 9/14 - 3/5

 

There isn't any real easy Lowest Common Denominator save multiplying the two denominators together:

14 * 5 = 70

a = 9/14 * 5/5 - 3/5 * 14/14

a = 45/70 - 42/70

a = 3/70

 

Since the problem is asking in ratios, you're answer may end up being in the ratio form 3:70.