Question

an officer told his assistant to count a total of rupees 10710 made up of one rupee coins.he counts at rate of rupees180 per minute for half an hour .after that he counts at the rate of rupees3 less every minute then the preceeding minutes. find the total time taken by the assistant to coumt the entire money?​

Answer 1

Total 1 hour 30 minutes taken by assistant to count the entire money.

Step-by-step explanation:

An officer told his assistant to count a total of rupees 10710 made up of one rupees coins.

He counts at the rate of 180 rupees per minute for half an hour.

He counted rupees in 30 minutes = 180 × 30

                                                        = 5400 Rupees

Now the amount left to be count  = 10,710 - 5400 = Rs. 5,310

After 30 minutes assistant count 3 rupees less every minute then the proceeding minutes.

31st minute = 177 coins

32nd minute = 174 coins

33rd minute = 171 coins

An arithmetic progression series formed 177, 174, 171, 168............ 5310 coins

First term a = 177 and Common difference = 177 - 180 = (-3)

Sum of n terms = $\frac{n}{2}[2a+(n-1)d]$

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

$5310=\frac{n}{2}[354-(n-1)3]$

$10620=n[354-3n+3]$

10620 = n(357 - 3n)

3540 = n(119-n)

n² - 119n + 3540 = 0

n² - 60n - 59n + 3540 = 0

n(n-60) - 59(n-60) = 0

(n-59) (n-60) = 0

n = 59, 60

Total time = 30 minutes + 60 minutes = 90 minutes or 1:30 minutes

Total 1 hour 30 minutes taken by assistant to count the entire money.

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