Question

(ii) The mean of the age of three students Vijay, Rahul and Rakhi is 15 years. If their
ages are in the ratio 4:5:6 respectively, then find their ages.
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Answer 1

$\sf{Solution}$

Step by step explanation :-

Given :-

• Mean of three students is 15 years
• Ages of their ratio are 4 : 5 : 6

To find :-

• Ages of the three students

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Formula to know :-

Mean = $\sf\dfrac{Sum\: of \: observations}{No \: of \: observations}$

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Sum of observations =

Hence their ages are in ratio 4 : 5 : 6

Let

Age of Vijay be 4x

Age of Rahul be 5x

Age of Rakhi be 6x

Sum of their ages = 4x + 5x + 6x

Sum of their ages = 15x

Sum of observations = 15x

No.of observations = Total no.of students

No.of observations = 3

Mean of their ages = 15

So,

Mean = $\sf\dfrac{Sum\: of \: observations}{No \: of \: observations}$

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

Do cross multiplication

15 (3) = 15x

45 = 15x

x = 45 /15

x = 3

Age of Vijay = 4x = 4(3)

Age of vijay = 12 years

Age of Rahul = 5x = 5 (3)

Age of rahul = 15 years

Age of Rakhi = 6x = 6(3)

Age of rakhi = 18 years

So, finally

• Age of vijay = 12 years
• Age of rahul = 15 years
• Age of rakhi = 18 years

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Verification :-

Hence we got ages of three students Their mean of age should be equal to 15

So,

$\sf\dfrac{12 + 15 + 18}{3}$ = 15

$\sf\dfrac{45}{3}$ = 15

15 = 15

LHS = RHS

Verified !