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(in minutes) by him to count the entire amount.

Answer 1

Total amount to be counted $=Rs.10710$

A man counts $Rs.180$ per minute for half an hour

Amount counted in half an hour $=180\times 30=Rs.5400$

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.

i.e., $177+174+171+......+3=5310$

Now this forms an arithmetic progression

where $a=177$ $d=3$

sum of n terms of $A.P=5310$

$S_n=\frac{n}{2}[a+l]=5310$

$\Rightarrow \frac{n}{2}[177+3]=5310$

$\Rightarrow n=59$

Total time $=30+59=89$ minutes