Question

the age of the boy in gruop are in A.P. with common difference of 3 months . The age of the youngest boyis 12 years. The sum of the age of all boys in group is 375 years. find the number of boys in the group

Answer 1

given common difference d = 3 months Youngest boy = 12 years old a = 12 years = 12 × 12 =144 months Sn = 375 years = 375 × 12 = 4500 months Sn = n/2 [2a + (n - 1) d] 4500 = n/2 [(2 × 144) + (n - 1) 3] 4500 × 2 = n [288 + 3n - 3 ] 9000 = 3n^2 + 285n i.e. 9000 is equal to 3n square plus 285n Dividing by 3 on both sides n^2 + 95n - 3000 = 0 n^2 + 120n - 25n - 3000 = 0 n (n + 120) - 25 (n + 120) = 0 (n + 120) (n - 25) = 0 n = - 120 or n = 25 Total no of student never negative Hence n = 25 is the correct answer

Answer 2

Answer:

243

Step-by-step explanation:

We are given that the age of the boy in group are in A.P.

Common Difference d = 3

The age of the youngest boy is 12 years.

So, first term = $a=12$

Let the total number of boys be n

The sum of the age of n boys in group is 375 years

Sum of first n terms in A.P. = $\frac{n}{2} (2a+(n-1)d)$

So, sum of age of n boys = 375

So,  $375 = \frac{n}{2} (2(12)+(n-1)3)$

$375 = \frac{n}{2} (24+3n-3$                                                

$750= 21+3n$            

$750-21=3n$          

$729=3n$          

$243=n$        

Hence the number of boys in a group is 243.