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In a society, a yoga instructor was hired to train the people of the society to live a healthy lifestyle. Yoga sessions were held daily from $5 \text{ p.m.}$ to $7 \text{ p.m.}$ in the society park. On day one, $5$ people joined the yoga session, on day two, $3$ more people joined, on day three, another $3$ people joined and in this manner every next day, $3$ more people kept on joining. Based on the given information, answer the following questions :
(i) On which day did $59$ people join the yoga session ?
(ii) How many people joined the yoga session on the $31^{\text{st}}$ day ?
(iii) (a) The yoga instructor was paid ₹100 for each person attending the yoga session. On which day would he earn ₹5,000 ?
OR
(b) What was the total amount earned by the yoga instructor in $16$ days ?
(i) On which day did $59$ people join the yoga session ?
(ii) How many people joined the yoga session on the $31^{\text{st}}$ day ?
(iii) (a) The yoga instructor was paid ₹100 for each person attending the yoga session. On which day would he earn ₹5,000 ?
OR
(b) What was the total amount earned by the yoga instructor in $16$ days ?
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Solution:
(i) $5 + (n - 1) 3 = 59 \Rightarrow n = 19$
(ii) $a_{31} = 95$
(iii) (a) Number of persons $= \frac{5000}{100} = 50$
$5 + (n - 1) 3 = 50 \Rightarrow n = 16$
OR
(iii) (b) $S_{16} = \frac{16}{2} [ 10 + 15 (3)] = 440$
Total amount earned in $16$ days $= 440 \times 100 = \text{Rs} 44000$
(i) $5 + (n - 1) 3 = 59 \Rightarrow n = 19$
(ii) $a_{31} = 95$
(iii) (a) Number of persons $= \frac{5000}{100} = 50$
$5 + (n - 1) 3 = 50 \Rightarrow n = 16$
OR
(iii) (b) $S_{16} = \frac{16}{2} [ 10 + 15 (3)] = 440$
Total amount earned in $16$ days $= 440 \times 100 = \text{Rs} 44000$