Question

Ages of two friends are in the ratio $ 2:1 $ . If the sum of their ages is 51 then their ages are
A.30 years, 20 years
B.34 years, 17 years
C.20 years, 10 years
D.30 years, 10 years

Answer 1

Hint: Ratio of the two quantities may be defined as the quantitative relation between the two amounts that tells us the number of times one of these quantities contains the other. Here in the question, the ages of two friends are given in the ratio $ 2:1 $ . That is, if you consider the age of one friend to be ‘X’ and the other to be ‘Y’ then $ X:Y = 2:1 $ . And sum of their ages that is, $ X + Y = 51 $ . Thus, we can very easily find their ages.

Complete step-by-step answer:
The following information is given in the question –
Ratio of the ages of two friends = $ 2:1 $
Sum of their ages = 51
Let us consider ‘x’ to be the common multiple.
Now, the ages of two friends are 2x and x.
As in the question it is given that the sum of their ages = 51
Thus, we can form a linear equation; from there we can easily get the value of ‘x’.
Now,
According to the question,
 $ \Rightarrow 2x + x = 51 \to \left( 1 \right) $
Solving the equation,
 $ \begin{array}{l}
\Rightarrow 3x = 51\\
\Rightarrow x = 17
\end{array} $
We get the value of.
Thus, putting the value of the common multiple we get the age of two friends.
 $ \Rightarrow 2x = 2 \times 17 = 34years $
 $ \Rightarrow x = 17years $

So, the correct answer is “Option B”.

Note: It becomes important for the students to have a good concept of ratio. Also solve the linear equation carefully to get the correct value of common multiple (x) as it is crucial for getting correct.