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 then the preceding minute. Find the entire time taken by him to count the entire amount.

• A. $56$ minutes
• B. $70$ minutes
• C. $89$ minutes
• D. $103$ minutes

Answer 1

Answer: (C)

$89$ minutes

Money counted in half an hours=$180\times 30=$ Rs. $5400$

then money left for counting =$10710-5400=$ Rs. $5310$

After half an hour he counted $3$ less per minute.

$\therefore$ rate of counting per minute $=$ $(180-3),(180-3-3).180-3-3-3).....$

$=177,174,\mathrm{171..}$

This form an A.P. whose first term $=177$ and difference $=-3$

Sum of A.P $=5310$

$\Rightarrow \frac{n}{2}[2a+(n-1\left)d\right]=5310$

$\Rightarrow \frac{n}{2}[2\times 177+(n-1\left)\right(-3\left)\right]=5310$

$\Rightarrow n[354-3n+3]=5310\times 2$

$\Rightarrow 357n-3n^2=10620$

$\Rightarrow 3n^2-357n+10620=0$

$\Rightarrow n^2-119n+3540=0$

$\Rightarrow n^2-59n-60n+3540=0$

$\Rightarrow n(n-59)-60(n-59)=0$

$\Rightarrow (n-59)(n-60)$

$\Rightarrow n=60$ or $n=59$

but $59<60$

$\therefore n=59$

Therefore, the time taken to count entire amount $=$ $30+59=89$ minute.