Question

Three numbers are in the ratio 4:5:6 and their average is 25. Then the largest number is:
A. 30
B. 32
C. 36
D. 42

Answer 1

Hint: In order to solve this problem assume a variable multiplied by the ratios of three numbers and then make an equation and solve according to the question.

Complete step-by-step answer:
The number which is in ratio is 4:5:6.
Then we can say that the three numbers may be 4a, 5a, 6a since the ratio of these three numbers is also 4:5:6.
Now, we have the three numbers as 4a, 5a, 6a.
It is given that the average of the three numbers is 25. So, we can do:
$\Rightarrow {\displaystyle \frac{\text{4a + 5a + 6a}}{\text{3}}}\text{ = 25}$
On solving further we get,
$$\begin{gathered} \Rightarrow {\displaystyle \frac{\text{15a}}{\text{3}}}\text{ = 25} \\ \Rightarrow \text{5a = 25} \\ \Rightarrow \text{a = }{\displaystyle \frac{\text{25}}{\text{5}}}\text{ = 5} \end{gathered}$$
So, a = 5 then the three numbers are 4(5)=20, 5(5)=25, 6(5)=30.
Therefore, the numbers are 20, 25, 30 and the highest number is 30.
So, the correct option is A.

Note: In this problem we should try to know that if the numbers are in the ratio then there might be something common in them which has been cancelled out when they are in the ratio, here we have assumed that number as ‘a’ then we have solve according to the condition provided and got the value of the highest number.