A manufacturer reckons that the value of a machine, which costs him ₹15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years

Solution:

The cost of the machine is ₹15625.

Machine depreciates by 20% every year. i.e., Its value after every year is 80% of the original cost i.e., 4/5 of the original cost.

Value at end of 5 years = 15625 x 4/5 x 4/5 x 4/5 x 4/5 x 4/5 = 15625 (4/5)⁵ = 5 x 1024 = 5120

Thus, the value of the machine at the end of 5 years is ₹ 5120.

Second method: 

We can solve this problem using a G.P. as well as the costs each year would form a G.P. 15625, 15625 x 4/5, 15625 x 4/5 x 4/5...

This is a G.P. where a = 15625 and r = 4/5.

Then the value at the end of 5 years is obtained by substituting n= 5 in the nᵗʰ term of a G.P. formula. Then we get

a₅ = 15625 (4/5)⁵ = 5 x 1024 = 5120

NCERT Solutions Class 11 Maths Chapter 9 Exercise ME Question 31

A manufacturer reckons that the value of a machine, which costs him ₹15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years

Summary:

The estimated value at the end of 5 years given that the machine costs ₹15626 and will depreciate each year by 20% would be ₹5120