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The best athlete of your school wants to participate in a $300$ m. race in a state championship. Presently he can run that distance in $60$ seconds but is confident that with each day of practice it will take him $3$ seconds less than the previous day. So, first day he will take $60$ seconds, $2^{nd}$ day $57$ seconds, third day $54$ seconds and so on, to complete the race. He wants to do it in $30$ seconds.
Based on the above, answer the following questions :
(i) Write the first five terms of time and show that it forms an A.P.
(ii) How much time he will take on $6^{th}$ day to complete the race?
(iii) (a) On which day he will be able to achieve his target of $30$ seconds?
OR
(b) If he devotes more time in practice and that may take him $3.2$ seconds less than the previous day in completing the race, then on which day he will be able to complete the race in $28$ seconds?
Based on the above, answer the following questions :
(i) Write the first five terms of time and show that it forms an A.P.
(ii) How much time he will take on $6^{th}$ day to complete the race?
(iii) (a) On which day he will be able to achieve his target of $30$ seconds?
OR
(b) If he devotes more time in practice and that may take him $3.2$ seconds less than the previous day in completing the race, then on which day he will be able to complete the race in $28$ seconds?
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Solution:
(i) $60, 57, 54, 51, 48$ (0.5 Mark)
This is an A.P. as common difference is $(-3)$ (0.5 Mark)
(ii) Required time = $45$ seconds (1 Mark)
(iii) (a) $a_n = 60 + (n-1) (-3) = 30$ (1 Mark)
$\Rightarrow n = 11$ (1 Mark)
OR
(b) $a_n = 60 + (n-1) (-3.2) = 28$ (1 Mark)
$\Rightarrow n = 11$ (1 Mark)
(i) $60, 57, 54, 51, 48$ (0.5 Mark)
This is an A.P. as common difference is $(-3)$ (0.5 Mark)
(ii) Required time = $45$ seconds (1 Mark)
(iii) (a) $a_n = 60 + (n-1) (-3) = 30$ (1 Mark)
$\Rightarrow n = 11$ (1 Mark)
OR
(b) $a_n = 60 + (n-1) (-3.2) = 28$ (1 Mark)
$\Rightarrow n = 11$ (1 Mark)