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.

Answer 1

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, S_n = 5310
Sum of n terms of AP is

$S_n=\frac{n}{2}(a+l)$
$5310=\frac{n}{2}(354+3)$
$n=59$

Hence the total time taken by the man to count the entire amount = 30 + 59
= 89 minutes or 1 hour 29 minutes