The value of a machine depreciates each year by 3 %. What will be the value of the machine bought for Rs 1,00,000 after two years.

1,000,000 / 1.03 = 970,873.79 After 1st Year

970,873.79 / 1.03 = 942,595.91 After 2nd Year

Two thirds rounded would be 66.67%. I'm uncertain whether you were asking about a straight line depreciation or some sort of degressive depreciation.

Basically, in a straight-line depreciation, you would calculate each depreciation as a fraction of your asset's original value. A machine worth $1000 in year 0 would depreciate annually with a constant amount of $100.

Your machine would be worth less than 66.67% of its original value after at least 4 years (4 x 10%). More precisely, 3 years and (33.3% x 365 days) 122 days.

Applying a degressive depreciation method, you would calculate the depreciation in each year as a fraction of your asset's residual value. This implies your depreciations would decrease each year (hence "degressive"). As soon as your depreciations fall below the amount you would depreciate in a straight line depreciation, you switch to the latter. The reason for this is that it does not really make sense for a company to depreciate it's assets with a lesser amount, given the tax benefits of depreciations and the time value of money.

Assuming the duration of the asset's useful life is 10 years, you would switch to the straight-line depreciations after the first year. This scenario would be equal to the straight-line depreciation: 3 years and 122 days.

In case the duration of the asset's useful life is shorter or longer than 10 years, the amount of time required for the asset to have less than two-thirds of its initial value depends on the duration of is life.

so basically the answer is

1,000,000 / 1.03 = 970,873.79 After 1st Year

970,873.79 / 1.03 = 942,595.91 After 2nd Year