Advertisement Remove all ads

A Piece of Equipment Cost a Certain Factory Rs 60,000. If It Depreciates in Value, 15% the First, 13.5% the Next Year, 12% the Third Year, and So On. What Will Be Its Value at the End of 10 Years, - Mathematics

Sum

A piece of equipment cost a certain factory Rs 60,000. If it depreciates in value, 15% the first, 13.5% the next year, 12% the third year, and so on. What will be its value at the end of 10 years, all percentages applying to the original cost?

Advertisement Remove all ads

Solution

In the given problem,

Cost of the equipment = Rs 600,000

It depreciates by 15% in the first year. So,

Depreciation in 1 year

= 600000 - 495000

=105000

=90000

It depreciates by 13.5% of the original cost in the 2 year. So,

Depreciation in 2 year  `= (13.5)/100 (600000) = 81000`

Further, it depreciates by 12% of the original cost in the 3 year. So,

Depreciation in 3 year  `= 12/100 (600000)=72000` 

So, the depreciation in value of the equipment forms an A.P. with first term as 90000 and common difference as −9000.

So, the total depreciation in value in 10 years can be calculated by using the formula for the sum of n terms of an A.P,

`S_n = n/2 [2a + (n-1) d]`

We get,

`S_n = 10/2 [2(90000) +(10-1)(-9000)]`

      `=10/2 [180000 + (9)(-9000)]`

      `=5(180000 - 81000)`  

     ` = 5(99000)`

       = 495000

So, the total depreciation in the value after 10 years is Rs 495000.

Therefore, the value of equipment = 600000 - 495000=105000 

So, the value of the equipment after 10 years is Rs 105,000 .

  Is there an error in this question or solution?
Advertisement Remove all ads

APPEARS IN

RD Sharma Class 10 Maths
Chapter 5 Arithmetic Progression
Exercise 5.6 | Q 68 | Page 54
Advertisement Remove all ads
Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×