Question -
Answer -
Given: Amount tobe counted is ₹ 10710
We need tofind time taken by man to count the entire amount.
He counts at the rateof ₹ 180 per minute for half an hour or 30 minutes.
So, Amount to becounted in an hour = 180 × 30 = ₹ 5400
Amount left = 10710 –5400 = ₹ 5310
Sn =5310
After an hour, rate ofcounting is decreasing at ₹ 3 per minute. This rate will form an A.P.
A.P. is 177, 174,171,……
Here a = 177 and d =174 – 177 = –3
By using the formula,
Sn =n/2 [2a + (n – 1)d]
5310 = n/2 [2(177) +(n-1) (-3)]
5310 = n/2 [354 -3n +3]
5310 × 2 = n [357 –3n]
10620 = 357n – 3n2
10620 = 3n(119 – n)
10620/3 = n(119 – n)
3540 = 119n – n2
n2 –119n + 3540 = 0
n2 –59n – 60n + 3540 = 0
n(n – 59) – 60(n – 59)= 0
(n – 59) (n – 60) = 0
n = 59 or 60
We shall considervalue of n = 59. Since, at 60th min he will count ₹ 0
∴ The total time takenby him to count the entire amount = 30 + 59 = 89 minutes.