Question
Three numbers are in the ratio 1 : 2 : 3. By adding 5 to
each of the numbers then the ratio changes to 2 : 3 : 4. The smallest number is:Solution
Let's denote the three numbers as a, 2a, and 3a. According to the problem, by adding 5 to each of these numbers, the new numbers become a + 5, 2a +5, and 3a+ 5. The new ratio is given as 2:3:4. Therefore, we can set up the following proportion equations: a+5/2 = (2a +5)/3 =3a +5/4 First, consider the ratio – a+5/2 = (2a +5)/3 3(a+5) = 2(2a +5) Expanding both sides: 3a + 15 = 4a + 10 a = 5. And that numbers – a =5 2a=10 3a=15. Smallest number is 5. Smart Approch- Old ratio=1:2:3 +1+1+1 New ratio=2:3:4 ATQ- 1=5unit Old numbers =5,10,15.
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