Question

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Answer 1

Here,

a = 12 yrs. = 144 months
d= 3 months
sn = 375 yrs. = 4500 months

Let, n = no. of boys

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

=> n/2[2a + (n-1)d] = 4500

=> n/2[2×144 + (n-1)×3] = 4500

=> n[288 + 3n -3] = 9000

=> n[3n + 285] = 9000

=> 3n^2 + 285n = 9000

=> 3{n^2 + 95n} = 3(3000)

=> n^2 + 95n = 3000

=> n^2 + 95n - 3000 = 0

=> n^2 + 120n - 25n - 3000 = 0

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

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

=> n = 25 OR -120

Since, the no. of boys can't be negative, so n = 25