Question

The average of four
consecutive even numbers is 27. Find the largest of thes numbers. ​

Answer 1

AnswEr :

• Let the Consecutive Even Numbers be n, (n + 2), (n + 4) and, (n + 6).
• Average of these numbers is 27.

• According to the Question Now :

⇒ Average × Number = Sum of Numbers

⇒ 27 × 4 = n + n + 2 + n + 4 + n + 6

⇒ 27 × 4 = 4n + 12

⇒ 27 × 4 = 4 × ( n + 3 )

• Dividing Both term by 4

⇒ 27 = ( n + 3 )

⇒ 27 - 3 = n

⇒ n = 24

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◑ n = 24

◑ (n + 2) = (24 + 2) = 26

◑ (n + 4) = (24 + 4) = 28

◑ (n + 6) = (24 + 6) = 30

∴ Hence, Numbers are 24, 26, 28 and 30.

Answer 2

$\LARGE\underline{\underline{\sf \red{T}\blue{o}\:\green{F}\orange{i}\pink{n}\red{d}:}}$ Find the largest numbers .. ?

$\LARGE\underline{\underline{\sf \red{G}\blue{i}\green{v}\orange{e}\red{n}:}}$

• Average of Four consecutive even numbers is 27.

We can solve it by 2 methods ..

First lets see basic Method .

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$\red{\bold{\underline{\underline{Solution(1)}}}}$

Let the four consecutive even Numbers be :--

2x, 2x+2 , 2x+4 and 2x+6

A/q,

Their average is Equal to 27 .

we know that ,

$\large\red{\boxed{\sf Average</strong><strong>={\frac{Total\:</strong><strong>sum</strong><strong>}{Total\:</strong><strong>Numbers</strong><strong>}}}}$

So,

$27 = \frac{2x + 2x + 2 + 2x + 4 + 2x + 6}{4} \\ \\ 8x + 12 = 27 \times 4 \\ \\ 8x = 108 - 12 \\ \\ x = \frac{96}{8} = 12$

So, Largest Number will be = 2x + 6 = 2×12 + 6 = 30 (Ans)

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$\red{\bold{\underline{\underline{Solution(2)}}}}$

Since Average of 4 even numbers is given 27 .

And we know that Average of the numbers is actually middle values of the numbers . (or mean)

if we have some numbers like 5,8,9,3,7,6

Their average will be exactly middle to them, that means average come when higher numbers give something to lower values , and vice versa ..

If we know this , we can solve this Question in 5 seconds .

Since all 4 are even numbers and 27 is their middle term.

so, our numbers will be ,

x1. x2. 27. x3. x4

Here, x1, x2, x3, and x4 are given Even numbers .

so , their values will be ..

24. 26. 27. 28. 30

So, our largest number is = 30 .

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$\huge\underline\mathfrak\green{Hope\:it\:Helps\:You}$

$\mathcal{BE\:\:BRAINLY}$