A clerk in a bank engaged in counting one rupee currency note. For the first 10 minutes quickly at a speed of Rs.150 per minute then he slows down and begins to count at a speed of Rs. 2 less
etery minute than previous minute. Find what time will he take to count a sum of Rs. 4500.

The time it would take the clerk to count a sum of Rs. 4,500 is 34 minutes

Step-by-step explanation:

The given parameters are;

The rate at which the clerk in the bank counted one rupee currency notes for the first 10 minutes =  Rs. 150/minute

After the first 10 minutes, the rate at which the clerk counted = Rs. 2 less than the previous minute

The time it will take the clerk to count Rs. 4,500 is given as follows;

The number of one rupee currency notes the clerk counts in the first 10 minutes = 10 × Rs. 150 = Rs. 1,500

The amount in one rupee currency notes the clerk counted at a decreasing rate of Rs. 2 less every minute = Rs. 4,500 - Rs. 1,500 = Rs. 3,000

From the 11th minute the number of rupees the clerk counts = Rs. 150 - Rs. 2 = Rs. 148

We have an arithmetic progression with the first term, a = 148, and the common difference, d = -2

The sum of n terms of an AP,

Which gives;

3000 = 149·t - t²

Which gives;

t² - 149·t + 3,000 = 0

(t - 24) × (t - 125) = 0, therefore, t = 24 minutes or t = 125 minutes

The time it would take the clerk to count a sum of Rs. 4,500 = 10 + 24 = 34 minutes.

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