Question

the value of a machine depreciates from rs. 32,768 to rs. 21,952 in three years. what is the rate % of depreciation? a. 11% b. 12.5% c. 33% d. 12.25%

Answer 1

if R is rate of depreciation of machine , P is the initial amount of machine , A is final amount of machine and n is the time taken to depreciate then use formula,

$\bf{A=P\left(1-\frac{R}{100}\right)^n}$

here, P = 32768 , A = 21952 and n = 3

then, 21952 = 32768(1 - R/100)³

21952/32768 = (1 - R/100)³

(28/32)³ = (1 - R/100)³

7/8 = 1 - R/100

1 - 7/8 = R/100

1/8 = R/100

R = 100/8 = 12.5 %

hence, option (b) is correct

Answer 2

A= P(1-R/100)^n

.

Principal= 32768

Amount = 21952

Time= 3years

.

21952= 32768(1-R/100)^3

21952/32768=( 1-R/100)^3

(28/32)^3 =( 1- R/100)^3

7/8 = 1-R/100

1/8 = R/100

R= 100/8 = 12.5%

.

option (b)