whats your counting time?
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 than the preceding minute .find the time taken by him to count the entire amount? (In minutes.)
The answer is 89.
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1 solution
During the first half-hour, he counts 1 8 0 ⋅ 3 0 = 5 4 0 0 which leaves 1 0 7 1 0 − 5 4 0 0 = 5 3 1 0 . The remaining balance is counted according to:
5 3 1 0 − Σ t = 1 T ( 1 8 0 − 3 t ) = 0 ;
or 5 3 1 0 − 1 8 0 T + 3 ⋅ 2 T 2 + T = 0 ;
or 2 3 T 2 − 2 3 5 7 T + 5 3 1 0 = 0 ;
or T 2 − 2 3 8 T + 3 5 4 0 = ( T − 5 9 ) ( T − 6 0 ) = 0 ;
or T = 5 9 , 6 0 .
Since 5 9 < 6 0 , he counts the entire amount in 3 0 + 5 9 = 8 9 minutes.