Question

The average age of a man and his son is 40 years, the ratio of their age is 7: 3, what is the mans age?

Answer 1

Answer:

Man's age = 56 years.

Step-by-step explanation:

Let the constant ratio be k.

So father's age = 7 k

and son's age = 3 k

Given their average is 40 years.

We know formula for Average = $\large \dfrac{Sum \ of \ numbers}{total \ number}$

Putting values in formula we get

$\large 40=\dfrac{7k+3k}{2}\\\\\\\large 80=10k\\\\\\\large k=8$

We get constant ration k = 8

Now father's age = 8 × 7 = 56 years.

Son's age = 8 × 3 = 24 years.

Thus we get answer.

Answer 2

☞ The average age of a man and his son is 40 years, the ratio of their age is 7: 3.

Let present age of Man be 7M and his son be 3M.

In this question we are talking about two persons.

Means total number is 2.

Average of man and his son age is 40.

• We have to find the age of Man.

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We know that

Average = $\dfrac{Sum\:of\:number}{Total\:number}$

Here sum of number is the.. sum of age of Man and his son.

=> 40 = $\dfrac{7M\:+\:3M}{2}$

=> 40 × 2 = 10M

=> 10M = 80

=> M = 8

• Age of man = 7M = 7(8) = 56 years.

• Age of his son = 3M = 3(8) = 24 years.

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Age of man = 56 years.

____________ $\bold{[ANSWER]}$

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✡ Put value of M in 40 = $\dfrac{7M\:+\:3M}{2}$

=> 40 = $\dfrac{10\:\times\:8}{2}$

=> 40 = $\dfrac{80}{2}$

=> 40 = 40

___________ [HENCE VERIFIED]