Question

Two numbers are in ratio 1: 3, if 5 is added to both the numbers, then the ratio becomes 1: 2. Find the sum of numbers?

Answer 1

Hint: Ratio is a number that is used to compare two quantities of the same unit or the same type. A ratio can be converted into a fraction accordingly as well to compare two terms. Since we have been given the ratio of two numbers that are unknown, therefore let us suppose that one of the numbers is x .

Complete step-by-step answer:
Therefore we can get the second number will be 3x from the given ratio.
 Further according to the question 5 has been added to both the numbers and on adding 5 to both the numbers x and 3x they become,
 $ x + 5 $ and $ 3x + 5 $
Then the final ratio becomes 1:2. Therefore it can be written as,
 $ \Rightarrow \dfrac{{x + 5}}{{3x + 5}} = \dfrac{1}{2} $
Cross multiplying we get,
 $ \Rightarrow 2(x + 5) = 1(3x + 5) $
On solving and moving all the constants on one side and the variables on the second side we get,
 $
   \Rightarrow 2x + 10 = 3x + 5 \\
   \Rightarrow 10 - 5 = 3x - 2x \\
   \Rightarrow x = 5 \;
 $
Hence one of the number is 5 and from the ratio 1:3 we can make out that the second number will be 3x so the second number is:
 $ \Rightarrow 3 \times 5 = 15 $
Hence the two numbers are 5 and 15 and we have been asked to find the sum of the two numbers, so on adding the two numbers we get,
 $
   \Rightarrow x + 3x = 4x \\
   \Rightarrow 5 + 15 = 20 \;
 $
Hence the sum of the two numbers is 20.
So, the correct answer is “20”.

Note: A ratio can be read carefully that is when we have a ratio is of the form a:b it is read as the ratio of a to b and it can be denoted in the fraction as $ \dfrac{a}{b} $ whereas the ratio b:a is read as the ratio of b to a and it can be denoted in fraction similarly by $ \dfrac{b}{a} $ .