Question

Of the three numbers, the first number is twice the second number and the second is thrice the third. If the average of the three numbers is 10, the largest number is:
A. 12
B. 15
C. 18
D. 30

Answer 1

Hint: In this question we have 3 numbers and one is inter- related to the other number. By reading the question we should make out a relation and should be written in the form of a numeral. By solving these relations, we can find the numbers.

Complete step-by-step answer:
In this we have three numbers, the first number is twice the second and second number is thrice the third. The first number is dependent on the second and second number is dependent on the third. Since both the first and second number depended on the third. Let the three numbers be \[a\] , \[b\] and \[c\] .
Let the third number be \[x\]
 \[ \Rightarrow c = x\]
The second number is thrice the third, therefore we have \[b = 3x\] .
The first number is twice the second, so we have \[a = 2(3x)\]
 \[ \Rightarrow a = 6x\]
Given, the average of three numbers is 10.
The average is defined as the ratio of total sum of all numbers to the number of items. Here we have three numbers and the average is 10
Therefore, we have \[\dfrac{{a + b + c}}{3} = 10\]
Substituting the values of \[a\] , \[b\] and \[c\] we have
 \[ \Rightarrow \dfrac{{6x + 3x + x}}{3} = 10\]
By adding, \[ \Rightarrow \dfrac{{10x}}{3} = 10\]
 \[ \Rightarrow 10x = 30\]
 \[ \Rightarrow x = 3\]
Therefore, the value of \[x\] is 3.
By substituting the value of \[x\] we can find the value of \[a\] , \[b\] and \[c\] .
So, we have \[a = 6 \times 3\] \[ \Rightarrow a = 18\]
And \[b = 3 \times 3\] \[ \Rightarrow b = 9\]
And \[c = x\] \[ \Rightarrow c = 3\]
We have to find the largest number among the three numbers. Now we have determined the three numbers and the numbers are 18, 9 and 3
Among these numbers the largest number is the first number and the first number is 18.
So, the correct answer is “Option C”.

Note: Students must carefully read the questions and find the relation between the numbers and convert the relations into numerals and simplify to find the numbers. By finding the unknown term we can find the numbers.
Formula for mean is given by:
Total number of sums of items/ Number of items