Chapter 9: Sequences And Series Miscellaneous Exercise

Given, the cost of the machine = Rs 15625

Also, given that the machine depreciates by 20% every year.

Hence, its value after every year is 80% of the original cost, i.e., 4/5^th of the original cost.

Therefore, the value at the end of 5 years =

= 5 × 1024 = 5120

Thus, the value of the machine at the end of 5 years will be Rs 5120.

Let’s assume x to be the number of days in which 150 workers finish the work.

Then from the question, we have

150x = 150 + 146 + 142 + …. (x + 8) terms

The series 150 + 146 + 142 + …. (x + 8) terms is an A.P.

With first term (a) = 150, common difference (d) = –4 and number of terms (n) = (x + 8)

Now, finding the sum of terms:

As x cannot be negative. [Number of days is always a positive quantity]

x = 17

Hence, the number of days in which the work should have been completed is 17.

But, due to the dropping out of workers, the number of days in which the work is completed

= (17 + 8) = 25