the ages of the boys in a group are in AP with the common difference of 3 months . the age of the youngest boy inthe group is 12 years . the sum of the ages of all the boys in the group is 375 year s . find the number of boys in the group.
Answers
Answered by
6
According to question
For the AP
a = 12
d = 3
S = 375
Number of boys = n
Thus
According to the formula of Sum of an AP
Sum S = n/2[2a + (n-1)d]
375 = n/2[ 2*12 + (n-1)3]
375 = n/2[ 24 + 3n - 3]
750 = n ( 21 + 3n)
750 = 21n + 3 n^2
3 n^2 + 21n - 750 = 0
n^2 + 7n - 250 = 0
n(n+7) = 250
n = 250 - 7 = 243
Thus number of boys = 243
For the AP
a = 12
d = 3
S = 375
Number of boys = n
Thus
According to the formula of Sum of an AP
Sum S = n/2[2a + (n-1)d]
375 = n/2[ 2*12 + (n-1)3]
375 = n/2[ 24 + 3n - 3]
750 = n ( 21 + 3n)
750 = 21n + 3 n^2
3 n^2 + 21n - 750 = 0
n^2 + 7n - 250 = 0
n(n+7) = 250
n = 250 - 7 = 243
Thus number of boys = 243
Similar questions