Question

K-The sum of three numbers is 60 and their ratio is \[1:2:3\], then the largest number is
A.60
B.10
C.20
D.30

Answer 1

Hint: Here we need to find the value of the largest number. We will first assume the three numbers to be any variable such that their ratios remain the same. Then we will find the sum of the three numbers and equate it with the given sum. After solving the equation obtained, we will get the required answer.

Complete step-by-step answer:
It is given that the ratio between the numbers \[1:2:3\].
Let the first number be \[x\], the second number be \[2x\] and the third number be \[3x\].
It is given that the sum of these three numbers is equal to 60.
So we can write it as
\[x + 2x + 3x = 60\]
Now, we will add the like terms present in the left hand of the equation. Therefore, we get
\[ \Rightarrow 6x = 60\]
On dividing both sides by the number 6, we get
\[\begin{array}{l} \Rightarrow \dfrac{{6x}}{6} = \dfrac{{60}}{6}\\ \Rightarrow x = 10\end{array}\]
Now, we will substitute the value of the variable in the assumed numbers.
First number \[ = x = 10\]
Second number \[ = 2 \times x = 2 \times 10 = 20\]
Third number \[ = 3 \times x = 3 \times 10 = 30\]
We can see that the value of the largest number is 30.
Hence, the correct option is option D.

Note: Here we have been provided the ratio of three numbers. When a fraction is written in \[a:b\] form such that \[a\] is the numerator and \[b\] is the denominator, then it is called ratio. In some situations, it shows the relation between the bigger and smaller numbers or in other words, it shows a comparison between two quantities. In real life, we use ratio in measuring the speed, rate of material, etc.