Question

Three numbers are in the ratio 4:5:6 and their
average is 30. The largest number is
(A) 28
(B) 32
(C) 36
(D) 42​

Answer 1

Answer:

36(c) is the right ans

Answer 2

Given :-

Ratio of the three numbers = 4 : 5 : 6

Average of the three numbers = 30

To Find :-

The largest number.

Analysis :-

Consider the common ratio as a variable. Then multiply it to each of the sides.

Substitute the given in the formula of mean average and find the sides accordingly.

Solution :-

Let the common ratio be 'x'. Then the sides would be 4x, 5x and 6x.

By the formula,

$\underline{\boxed{\sf Mean \ average=\dfrac{Sum \ of \ values}{Number \ of \ values} }}$

Given that,

Ratio of the three numbers = 4 : 5 : 6

Average of the three numbers = 30

Substituting their values,

$\sf \dfrac{4x+5x+6x}{3} =30$

$\sf =\dfrac{15x}{3} =30$

By dividing,

$\sf =5x=30$

Finding the value of x,

$\sf x=\dfrac{30}{5}$

$\sf x=6$

Therefore, the value of x is 6.

Finding the numbers,

$\sf 4x= 4 \times 6=24$

$\sf 5x=5 \times 6=30$

$\sf 6x=6 \times 6=36$

Therefore, the numbers are 24, 30 and 36.

Largest number is 36.