(Q7).A machine costs Rs. 5,00,000. If the value depreciates 15% in the first year, 13
1
2
 % in the second year, 12% in the third year and so on. What will be its value at the end of 10 years, when all the percentages will be applied to the original cost?

Given: Cost price of a machine = Rs. 5,00,000

Depreciation during the years

Year 1 2 3 ....... 10
Depreciation
1

Sum of the depreciations =

15 + 13
1
2
 + 12 + ...... + 10 terms

a = ; d = a2 - a1

=
1
 - = -
1
 -
Sn =
n
2
 [2a + (n - 1)d]
S10 =
2
 [2 × + ( - 1)(
-
 )]
= [ -
2
 ] = ×
( - )
2
=
×
2
 =
2
 = %

∴ Cost after 10 years = (100 – )% of 5,00,000

= % of 5,00,000

=
× 500000
2

= Rs.

∴ The value at the end of 10 years will be Rs. .