Question

The cost of a machine depreciated by Rs 4000 during the first year and by Rs 3600

during the second year. Calculate:

i) The rate of depreciation

ii) The original cost of the machine

iii) The cost at the end of the third year.​

Answer 1

Step-by-step explanation:

2 From 1 and 2 , we get 4000 1 - R 100 = 3600 ⇒ 40 100 - R = 3600 ⇒ 100 - R = 90 ⇒ R = 10 So , rate of depriciation = 10 % p . a . From. Now , amount at the end of 3 years is A 3 = P 1 - R 100 3 = 40000 1 - 10 1000 3 = 29160 So , cost of the machine after the end of third year = Rs 29 , 160 .Mar 17, 2016

Answer 2

Answer:

Step-by-step explanation:

Let P is the original cost of machine.

Let R be the rate of depriciation.

Let A1 be the cost of the machine after first year.

A1 = P[1 − R/100]

Now,

P − A1 = 4000

⇒P − P[1 − R100] = 4000

⇒P[1 − (1 − R100)] = 4000

⇒PR100 = 4000        .......(1)

Let A2 be the cost of machine after second year.

A2 = A1[1 − R100]

⇒A2 =P[1 − R100][1 − R100] = P[1 − R100]2

⇒A1 − A2 = 3600

⇒ P[1 − R100] − P[1 − R100]2 = 3600

⇒P(1 − R100)[1 − (1 − R100)] = 3600

⇒P(1 − R100)(R100) = 3600

⇒PR100(1 − R100) = 3600    ......(2)

From (1) and (2),

we get 4000(1 − R100) = 3600

⇒40(100−R) = 3600

⇒100−R = 90

⇒R = 10

So,

rate of depriciation = 10%

p.a.

From (1),

we get

PR100 = 4000

⇒P × 10100 = 4000

⇒P = 40,000 So, original cost of the machine = Rs 40000.

Now, amount at the end of 3 years is

A3 = P[1 − R100]3=40000[1 − 101000]3= 29160

So,

cost of the machine after the end of third year = Rs 29,160.