Question

A man is employed to count rupees 10710 account at the rate of Rs 180 per minute for half an hour after this rate of rupees 3 less every minute and than the preceding minutes find the time taken by him to count the entire amount

Answer 1

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….

Answer 2

amount counted in half an hour = Rs 180 * 30 = Rs.5400

so the remaining to be calculated is = Rs10710 - Rs 5400 = Rs 5310

now as the speed is decreasing uniformly every minute by Rs3 so it forms an AP series.

where a=Rs177 ; d=-3 ; s=Rs 5310 ; n=?

5310 = n/2 [354+(n-1)-3]

10620 = n[357-3n]

3n^2 -357n +10620 = 0

n^2 - 119n + 3540 = 0

by using deteminant method ,

d = 1

then the roots are 59 and 60.

so we will use 59 because these are minutes

and ithe work is in 59 min.

atlast, the total time to calculate the whole amount is = 59min + 30min = 1hr 29min ANS

Hope it helps you.

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