A man is employed to count ₹ 10710. He counts at the rate of ₹ 180 per minute for half an hour. After this he counts at the rate of ₹ 3 less every minute then the preceding minute. Find the time taken by him to count the entire amount.
Given: Amount to be counted is Rs. 10710
To find: Time taken by man to count the entire amount
He counts at the rate of Rs. 180 per minute for half an hour or 30 minutes
Amount to be counted in an hour = 180 * 30 = Rs. 5400
Amount to be left = 10710 – 5400 = 5310
⇒ Sn = 5310
After an hour, rate of counting is decreasing at Rs. 3 per minute. This rate will form an A.P.
A.P. will be 177, 174, 171,……………………
Here a = 177 and d = 174 – 177 = –3
Formula used:
where a is first term, d is common difference and n is number of terms in an A.P.
Therefore,
⇒ 10620 = 3n(119 – n)
⇒ n2 – 59n – 60n + 3540 = 0
⇒ n(n – 59) – 60(n – 59) = 0
⇒ (n – 59)(n – 60) = 0
⇒ n = 59 or 60
We will take value of n = 59 as at 60th min he will count Rs.0
Therefore, total time taken by him to count the entire amount = 30 + 59 = 89 minutes