Question

The average age of Ram, Shyam and Ghanshyam is 20 years and their age ratio is 2: 3: 5, then what is the age of Ram​

Answer 1

★ AnswEr :-

• 12 years

★ GivEn :-

• The average age of Ram, Shyam and Ghanshyam is 20 years.
• Their age ratio is 2: 3: 5

★ To Find :-

• The age of Ram

$\star \: \boxed{ \red{Solution:-}}$

➠ According to the question,

➠ The age ratio of Ram, Shyam and Ghanshyam is 2 : 3 : 5.

➠ Let the common factor of the ratio be x ( ≠ 0 )

➠ Therefore, the ages of,

• Ram ➦ 2x years
• Shyam ➦ 3x years
• Ghanshyam ➦ 5x years

➠ As given, the average age of them is 20 years.

➠ We know,

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

➠ Therefore, we get,

$\implies \sf \: \dfrac{2x + 3x + 5x}{3} = 20$

$\implies \sf \: 10x = 3 \times 20$

$\implies \sf \: x = \dfrac{60}{10}$

$\implies\boxed{ \sf {\red {\bold{x = 6}}}}$

➠ Now, age of Ram = 2 × 6 = 12 years.

$\boxed{ \sf{ \red{ \bold{Age_{Ram} = 12 \: years}}}}$

★ Verification :-

➠ Ages of,

• Ram ➦ 12 years
• Shyam ➦ 6 × 3 = 18 years
• Ghanshyam ➦ 6 × 5 = 30 years

➠ Sum of their age = 12 + 18 + 30 = 60 years.

➠ Average age = 60 ÷ 3 = 20 years.

Hence, Verified!

Answer 2

Answer:

Given :-

• The average age of Ram, Shyam and Ghanshyam is 20 years and their ratio is 2:3:5.

To Find :-

• What is the age of Ram.

Solution :-

✧ Age of Ram be 2x

✧ Age of Shyam be 3x

✧ Age of Ghanshyam be 5x

And, their average age is 20 years.

According to the question,

⇒ $\sf\dfrac{2x + 3x + 5x}{3}$ = 20

⇒ $\sf\dfrac{10x}{3}$ = 20

By doing cross multiplication we get,

⇒ 10x = 3(20)

⇒ 10x = 60

⇒ x = $\sf\dfrac{\cancel{60}}{\cancel{10}}$

➠ x = 6

Hence, their required ages will be,

✧ Age of Ram = 2x = 2(6) = 12 years

✧ Age of Shyam = 3x = 3(6) = 18 years

✧ Age of Ghanshyam = 5x = 5(6) = 30 years

$\therefore$ The age of Ram is 12 years .

⍟︎ Let's Verify :-

↦ $\sf\dfrac{2x + 3x + 5x}{3}$ = 20

Put x = 6

↦ $\sf\dfrac{2(6) + 3(6) + 5(6)}{3}$ = 20

↦ $\sf\dfrac{12 + 18 + 30}{3}$ = 20

↦ $\sf\dfrac{60}{3}$ = 20

By doing cross multiplication we get,

↦60 = 3(20)

➠ 60 = 60

➥ LHS = RHS

Hence, Verified ✔