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.   Mr. Durani bought a plot of land for Rs. 180000 and a car for Rs. 320000 at the same time. The value of the plot of land grows uniformly at the rate of 30% p.a., while the value ofthe car depreciates by 20% in the first year and by 15% p.a. thereafter. If he sells the plot of land as well as the car after 3 years, what will be his profit or loss? Ans: (Profit ofRs. 80420)

Dear Student,

Please find below the solution to the asked query:

Given : Mr. Durani bought a land for Rs 180000 and the value of land grows uniformly by 30 % per annum .

We know formula for compound interest :  Amount =  P${\left(1 + \frac{r}{100}\right)}^t$ , So

Cost of land after three years = 180000${\left(1 + \frac{30}{100}\right)}^3 = 180000{\left(1 + \frac{3}{10}\right)}^3 = 180000{\left(\frac{13}{10}\right)}^3= 180000{\left(1.3\right)}^3= 180000 \times 2.197$ = 395460

And

Mr. Durani also bought a car for Rs 320000 and the value of car depreciates 20 % for first year and 15 % thereafter

We know formula for compound interest when we have succesive rate that are depreciates   :  Amount =  P$\left\{\left(1 - \frac{r_1}{100}\right)\left(1 - \frac{r_2}{100}\right)...\right\}$ , So

Cost of car after three years = 320000$\left(1 - \frac{20}{100}\right)\left(1 - \frac{15}{100}\right)\left(1 - \frac{15}{100}\right)= 320000\left(1 - \frac{1}{5}\right)\left(1 - \frac{3}{20}\right)\left(1 - \frac{3}{20}\right) = 320000 \times \frac{4}{5}\times \frac{17}{20}\times \frac{17}{20}=160 \times 4 \times 17 \times 17$ = 184960

Then,

Mr . Durani gets total profit of loss in all transiction  =  395460 + 184960 - 180000 - 320000 = 80420 ( That is positive so Mr . Durani gets profit )

Therefore,

Total profit Mr. Durani gets  =  Rs . 80420                                                                       ( Ans )


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