Question

the average of 3 boys is 16 years If their ages are in the ratio 4:5:7 then the age of youngest boys is ?​

Answer 1

AnswEr :

• Let the Boys be A, B & C and, their respective ages be 4n, 5n & 7n
• Average Age of Boys = 16 years

$\bigstar\:\boxed{\sf Average = \dfrac{Sum \:of \:Terms}{Number \:of \:Terms}}$

$\rule{100}{2}$

• According to the Question Now :

$:\implies\sf Average = \dfrac{Sum \:of \:Terms}{Number \:of \:Terms} \\\\\\:\implies\sf 16 = \dfrac{4n + 5n + 7n}{3}\\\\\\:\implies\sf 16 \times 3 = (4n + 5n + 7n)\\\\\\:\implies\sf 16 \times 3 = 16n\\\\\\:\implies\sf \cancel\dfrac{16 \times 3}{16} = n\\\\\\:\implies\sf n = 3$

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• A G E S ⠀O F ⠀B O Y S :

◗ A = 4n = 4(3) = 12 years

◗ B = 5n = 5(3) = 15 years

◗ C = 7n = 7(3) = 21 years

⠀

∴ Hence, Age of youngest boy is 12 years.

Answer 2

$\huge{\underline{\underline{\red{\mathfrak{Answer :}}}}}$

★ Average age of Boys = 15

★ Ratio of ages of boys is 4:5:7

Let the ages be

4x , 5x and 7x

Now use formula for average

$\large \star {\underline{\boxed{\sf{Average \: = \: \dfrac{Sum \: of \: observations}{Number \: of \: Observation}}}}}$

⇒16 = 4x + 5x + 7x/3

⇒16 = 16x/3

⇒16*3 = 16x

⇒48 = 16x

⇒x = 48/16

⇒x = 3

$\rule{200}{2}$

Ages of boys are :

1. 4x = 4(3) = 12 years
2. 5x = 5(3) = 15 years
3. 7x = 7(3) = 21 years

∴ Youngest age is of 12 years boy