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Case Study - 3
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
(iii) (b) What was the total amount earned by the yoga instructor in $16$ days ?
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
(iii) (b) What was the total amount earned by the yoga instructor in $16$ days ?
Show SolutionHide Solution↓
(i) $5 + (n - 1) 3 = 59 \Rightarrow n = 19$ [$1$ mark]
(ii) $a_{31} = 95$ [$1$ mark]
(iii) (a) $\text{Number of persons} = \frac{5000}{100} = 50$ [$1$ mark]
$5 + (n - 1) 3 = 50 \Rightarrow n = 16$ [$1$ mark]
OR
(iii) (b) $S_{16} = \frac{16}{2} [10 + 15(3)] = 440$ [$1$ mark]
$\text{Total amount earned in } 16 \text{ days} = 440 \times 100 = \text{\text{Rs} } 44000$ [$\frac{1}{2} + \frac{1}{2}$ mark]
(ii) $a_{31} = 95$ [$1$ mark]
(iii) (a) $\text{Number of persons} = \frac{5000}{100} = 50$ [$1$ mark]
$5 + (n - 1) 3 = 50 \Rightarrow n = 16$ [$1$ mark]
OR
(iii) (b) $S_{16} = \frac{16}{2} [10 + 15(3)] = 440$ [$1$ mark]
$\text{Total amount earned in } 16 \text{ days} = 440 \times 100 = \text{\text{Rs} } 44000$ [$\frac{1}{2} + \frac{1}{2}$ mark]