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. 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

The man 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 preceding minute.

Then, the amount counted in first 30 minute

$=Rs.180\times 30=Rs.5400\dots \dots \left(i\right)$

The amount left to be counted after 30 minute

= Rs. 10710 - 5400 = Rs. 5310 .... (ii)

ATQ

A.P formed is $(180-3)+(180-2\times 3)+\dots \dots =5310$

Let time taken to count 5310 be t

Then,

$S_1=\frac{t}{2}\left[\right(180-3)+(t-1\left)\right(-3\left)\right]$

$5310=\frac{t}{2}[200-3t]$

Or t = 59 minute

Thus, the total time taken by the man to count Rs. 10710 is (59+30) = 89 minutes.