Question

the ages of student in a group of an a.p is not known d is 3 a is 12
sum of ages of students is 375​

Answer 1

Answer:

Solution :-

Let the number of boys in the group be 'n'

Given - First term 'a' = 12 (Age of youngest boy is 12 years)

Common difference = 3 months = 3/12 years = 1/4 years

Sn = 375 years

Sn = n/2[2a + (n - 1)d]

375 = n/2[2*12 + {(n - 1)1/4}]

375*2 = n[24 + {(n - 1)/4}]

750 = [{24n/1} + {(n² - n)/4}]

750 = (96n + n² - n)/4

750*4 = n² + 95n

n² + 95n - 3000 = 0

n² + 120 - 25n = 3000 = 0

n(n + 120) - 25(n + 120) = 0

(n + 120) = 0 or (n - 25) = 0

n = - 120 or n = 25

Number of boys cannot be negative so, the correct value of n is 25.

Hence, total number of boys in the group is 25

Answer 2

Answer::

Given in the attachment.