A man employed to count Rs 10710 - He counts at the rate of Rs 180 per minute for half an hour- After this he counts at the rate of Rs 3 less every minute than the preceding minute- Find the time taken by him to count the entire amount-My solution-Total sum -10710In 30 mins -180 - 30-Rs 5400Money left to count -10710-5400 -5310S n -n - 22 - 177- n -1-35310-n - 2354-3-3 n5310 - 2-357 n-3 n210620-3119 n-n23540-119 n-n2n -119 - V 119- 2-413540- 2 n -119 -14161-14160- 2n -119-1 - 2- 119-1 - 2n -60-59Final answer should be 60-30 or 59-30 But the final answer is given as only 59-30How-

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A man was employed to count $R s 10710$ . He counts at the rate of $R s 180$ per minute for half an hour. After this, he counts at the rate of $R s 3$ less every minute than the preceding minute . Find the time taken by him to count the entire amount.

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Solution

Amount to be counted $= R s 10710$
Man counts $R s 180 p e r m i n u t e$ for half an hour
Amount counted in $30 m i n = 30 \times R s 180 = R s 5400$
Amount to be counted $= R s 10710 - R s 5400 = R s 5310$
It is also given that after half an hour $R s 3$ gets less every minute than the preceding minute.
The $A P$ becomes, $177 + 174 + 171 \dots + 3 = 5310$
Here $a = 177, d = 174 - 177 = - 3, S_{n} = 5310$
Sum of n terms of $A P$ is $= 90 n$
$\Rightarrow 5310 = 90 n ∴ n = 59$
Hence the total time taken by the man to count the entire amount $= 30 + 59 = 89 m i n u t e s$ or $1 h o u r 29 m i n u t e s$

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A man was employed to count Rs10710. He counts at the rate of Rs180 per minute for half an hour. After this, he counts at the rate of Rs3 less every minute than the preceding minute . Find the time taken by him to count the entire amount.

A man was employed to count $R s 10710$ . He counts at the rate of $R s 180$ per minute for half an hour. After this, he counts at the rate of $R s 3$ less every minute than the preceding minute . Find the time taken by him to count the entire amount.