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Question

# A man is 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.

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Solution

## Amount to be counted = Rs 10710 Man counts Rs 180 per minute for half an hour Amount counted in 30 min = 30 × Rs 180 = Rs 5400 Amount to be counted = Rs 10710 – Rs 5400 = Rs 5310 It is also given that after half an hour Rs 3 gets less every minute than the preceding minute. The AP becomes, 177 + 174 + 171 … + 3 = 5310 Here a = 177, d = 174 – 177 = - 3, Sn = 5310 Sum of n terms of AP is Sn=n2(a+l) 5310=n2(354+3) n=59 Hence the total time taken by the man to count the entire amount = 30 + 59 = 89 minutes or 1 hour 29 minutes

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