Question
Three numbers are in the ratio 2: 3: 5. By adding 7 to
each of the numbers then the ratio changes to 3: 4: 6. The smallest number is:Solution
Let's denote the three numbers as 2a, 3a, and 5a. According to the problem, by adding 7 to each of these numbers, the new numbers become 2a + 7, 3a +7, and 5a+ 7. The new ratio is given as 3:4:6. Therefore, we can set up the following proportion equations: 2a+7/3 = (3a +7)/4 =5a +7/6 First, consider the ratio – 2a+7/3 = (3a +7)/4 4(2a+7) = 3(3a +7) Expanding both sides: 8a + 28 = 9a + 21 a = 7. And that numbers – 2a =14 3a=21 5a=35. The smallest number is 14. Smart Approach- Old ratio =        2         :3        :5                        +1       +1       +1 New ratio =      3         :4        :6 ATQ- 1=7unit Old numbers =14,21,35.
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