HOTS The ages of the students in a class are in APwhose common differe

1.	HOTS The ages of the students in a class are in APwhose common difference is 4 months. If theyoungest student is 8 yr old and the sum of theages of all the students is 168 yr, then find thenumberof students in the class.
Answer» Let us first convert all years in months. 8yrs. = 96 months, 168yrs. = 2016 months. Therefore A.P. = 96,100,104.... Now, a = 96 S = 2016 d = 4 n=? S = n/2( 2a + (n-1)d) 2016 = n/2( 192 + n-1)4) 4032 = n( 192 + 4n-4) 4032 = 4n2+188n 4n2+188n - 4032 = 0 n = [47 +/- ?(2209+4032)]/ (? means under root) n = [47+/- ?(6241)] / 2 n = (47+/- 79) / 2 n = (47+ 79) / 2 or n = (47-79) / 2 Now the latter option is not possible as no. of students can never be negative. Therefore n = (47+79) / 2 n = 169 / 2 Therefore n = 63

HOTS The ages of the students in a class are in APwhose common difference is 4 months. If theyoungest student is 8 yr old and the sum of theages of all the students is 168 yr, then find thenumberof students in the class.

Answer»

Let us first convert all years in months.

8yrs. = 96 months, 168yrs. = 2016 months.

Therefore A.P. = 96,100,104....

Now, a = 96

S = 2016

d = 4

n=?

S = n/2( 2a + (n-1)d)

2016 = n/2( 192 + n-1)4)

4032 = n( 192 + 4n-4)

4032 = 4n2+188n

4n2+188n - 4032 = 0

n = [47 +/- ?(2209+4032)]/ (? means under root)

n = [47+/- ?(6241)] / 2

n = (47+/- 79) / 2

n = (47+ 79) / 2 or n = (47-79) / 2

Now the latter option is not possible as no. of students can never be negative.

Therefore n = (47+79) / 2

n = 169 / 2

Therefore n = 63