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 by him to count the entire amount.
Answers
Answer:
The time taken by him to count the entire amount is 1 hr 29 min.
Step-by-step explanation:
Given :
A man is employed to count = ₹ 10710
In 1 minute a man counts = ₹ 180
In half an hour (30 minutes) a man counts = ₹ 180 × 30 = ₹ 5400
Amount left to be counted after half an hour, Sn= 10710 – 5400 = ₹ 5310
In 31st min a man count 3 less than preceding minute = 180 – 3 = ₹ 177
In 32nd min a man count 3 less than preceding minute = 177 – 3 = ₹ 174
Arithmetic progression (A.P) formed is 177, 174,……..5310
Here, a = 177 , d = 174 – 177 = -3
By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]
5310 = (n/2) [2(177) + (n - 1) -3]
5310 × 2 = n [354 - 3n + 3]
10620 = 354n – 3n² + 3n
10620 = 357n – 3n²
⇒ 3n² – 357n + 10620 = 0
⇒ 3 (n² – 119n + 3540) = 0
⇒ n² – 119n + 3540 = 0
⇒ n² - 60n - 59n + 3540 = 0
[By middle term splitting]
⇒ n (n - 60) - 59 (n - 60) = 0
⇒ (n – 59) (n – 60) = 0
Therefore, n = 59 or n = 60
Here, we will use 59 because 59 are minutes and 60 becomes 1 hour.
Therefore, the total time taken to calculate the entire amount = 59 + 30 = 89 min i.e 1 hr 29 min
Hence, the time taken by him to count the entire amount is 1 hr 29 min.
HOPE THIS ANSWER WILL HELP YOU….
Step-by-step explanation:
Given :
A man is employed to count = ₹ 10710
In 1 minute a man counts = ₹ 180
In half an hour (30 minutes) a man counts = ₹ 180 × 30 = ₹ 5400
Amount left to be counted after half an hour, Sn= 10710 – 5400 = ₹ 5310
In 31st min a man count 3 less than preceding minute = 180 – 3 = ₹ 177
In 32nd min a man count 3 less than preceding minute = 177 – 3 = ₹ 174
Arithmetic progression (A.P) formed is 177, 174,……..5310
Here, a = 177 , d = 174 – 177 = -3
By using the formula ,Sum of nth terms , Sn = n/2 [2a + (n – 1) d]
5310 = (n/2) [2(177) + (n - 1) -3]
5310 × 2 = n [354 - 3n + 3]
10620 = 354n – 3n² + 3n
10620 = 357n – 3n²
⇒ 3n² – 357n + 10620 = 0
⇒ 3 (n² – 119n + 3540) = 0
⇒ n² – 119n + 3540 = 0
⇒ n² - 60n - 59n + 3540 = 0
[By middle term splitting]
⇒ n (n - 60) - 59 (n - 60) = 0
⇒ (n – 59) (n – 60) = 0
Therefore, n = 59 or n = 60
Here, we will use 59 because 59 are minutes and 60 becomes 1 hour.
Therefore, the total time taken to calculate the entire amount = 59 + 30 = 89 min i.e 1 hr 29 min
Hence, the time taken by him to count the entire amount is 1 hr 29 min.