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Class 10 › Mathematics › Arithmetic Progressions
CBSE2026Class Class 10 · Mathematics4 Marks · Long✅ Verified
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, 2nd day 57 seconds, third day 54 seconds and so on, to complete the race. He wants to do it in 30 seconds.
(i) Write the first five terms of time and show that it forms an A.P.
(ii) How much time will he take on the 6th day to complete the race?
(iii)(a) On which day will he be able to achieve his target of 30 seconds?
OR
(iii)(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 will he be able to complete the race in 28 seconds?
✅ Answer & Solution
(i) Times: 60, 57, 54, 51, 48 seconds. Since each term differs from the previous by a constant $-3$, this is an A.P. with $a=60,\ d=-3$.
(ii) $a_6=a+5d=60+5(-3)=60-15=45$ seconds.
(iii)(a) $a_n=30 \Rightarrow 60+(n-1)(-3)=30 \Rightarrow 3(n-1)=30 \Rightarrow n=11$. He will achieve his target on **Day 11**.
OR
(iii)(b) With $d=-3.2$: $60+(n-1)(-3.2)=28 \Rightarrow 3.2(n-1)=32 \Rightarrow n-1=10 \Rightarrow n=11$. He completes the race in 28 seconds on **Day 11**.
