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.

Explanation

Amount to be counted `=Rs10710`

Man counts `Rs180` perminute for half an hour

Amount counted in
`30min=30×Rs180=Rs5400`

Amount to be counted
`=Rs10710–Rs5400=Rs5310`

It is also given that after half an hour Rs3 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 =90n
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