Question

A machine valued rs 49074 is to be depriciated at 15% p.a of its value at the beginning of each year. when will the value be 20000 nd 1/10 th of original value​

Answer 1

Answer:

NOTE: Before solving this problem, we must get aware that in this type of problem, we use both the rules of compound and simple, decreasing or increasing formulas accordingly.

Solution:

Worth of the machine = Rs. 490740

Let, after n years, the machine's value would get reduced by 90% with 15% depreciation at the beginning of each year.

Therefore, after n years, the value would become

= Rs. 490740 * (1 - 15/100)ⁿ

= Rs. 490740 * (85/100)ⁿ

= Rs. 490740 * (0.85)ⁿ

Again, after n years, the value would get reduced by 90%,

i.e., the value of the machine after n years be

= Rs. 490740 * (1 - 90/100)

= Rs. 490740 * 10/100

= Rs. 49074

By the given condition,

490740 * (0.85)ⁿ = 49074

or, (0.85)ⁿ = 0.1

or, n * log(0.85) = log(0.1)

or, n = log(0.1) / log(0.85)

or, n ≈ 14.2

i.e., n = 14.2 years

= 14 years 2 months

∴ after 14 years 2 months, the machine's value would get reduced by 90%.

Answer 2

Answer:

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