the minimum age of children to be eligible to participate ina painting competiotion is 18years, it is observed tahtbthe age of yougest boy was 8 years and the ages of rest of participate are having a common difference of 4 months. if the sum of ages of all the participants is 168 years, find the age of eldest participant in pinating competiotion.
Answers
Step-by-step explanation:
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Answer:
13 years
Step-by-step explanation:
Given,
age of the young boy = 8 years
Ages of rest of participate are having C.D of 4 years.
Common difference between ages = 4 months
= 4/12 years
= 1/3 years .
Now,
First term, a = 8 years
Common difference will be d = 1/3.
Let the number of children be ‘n’.
Given, sum of ages = 168 year
Sₙ = 168
Also, we know sum of n terms of an AP
Sₙ = (n/2)[2a + (n - 1) * d]
Putting values, we get
168 = (n/2)[2 * 8 + (n - 1) * 1/3]
=> 336 = n[16 + (n - 1)/3]
=> 1008 = n(47 + n)
=> 47n + n² - 1008 = 0
=> n² + 47n - 1008 = 0
=> n² + 63n - 16n - 1008 = 0
=> n(n + 63) - 16(n + 63) = 0
=> (n + 63)(n – 16) = 0
=> n = 16 or n = -63 [number of students can’t be negative]
=> n = 16
Also, we know nth term of an AP:
aₙ = a + (n - 1) * d
=> a₁₆ = 8 + (n - 1) * 1/3
=> a₁₆ = 8 + (16 - 1)/3
=> a₁₆ = 39/3
=> a₁₆ = 13 years
Therefore,
Age of eldest student is 13 years.
Hope it helps!