A car valued at Rs. 400000 is insured for Rs. 250000. The rate of premium is 5% less 20%. How much loss does the owner bear including the premium if the value of the car is reduced to 60% of its original value?

Hint: We find out the loss of the car value for price deduction to 60% of its original value. We find the amount he can claim for having insurance. The extra amount he has to pay for premium also goes to the loss count. We evaluate the net loss from these three parts.

Complete step by step answer:
The car value is Rs. 400000. The insurance value is Rs. 250000. This is the policy value.
The rate of premium is 5% less 20% on the policy.
So, the premium value is in general \[\dfrac{250000\times 5}{100}=12500\].
20% of this premium value will be deducted. So, net premium value will be
\[12500\left( 1-\dfrac{20}{100} \right)=\dfrac{12500\times 4}{5}=10000\].
Now the value of the car is reduced to 60% of its original value i.e. Rs. 400000. The loss of price deduction will be the rest of the 40%.
The loss of the car value will be \[400000\left( 1-\dfrac{60}{100} \right)=\dfrac{400000\times 40}{100}=160000\].
For having insurance, he can claim that works with the theorem of $claim=loss\times \dfrac{policy}{property}$.
So, he claims Rs. $160000\times \dfrac{250000}{400000}=100000$.
He also has the premium. He pays a larger amount of $rate\times policy$.
So, extra payment will be \[\dfrac{250000\times 4}{100}=10000\].
So, the net loss will be $160000-100000+10000=70000$ Rs.

Therefore, the owner of the car loses Rs. 70000.

Note: The premium policy is for the price of the car. It changes with the price of the car.as he has to pay the price for it. The claim is the only profit he gets for price reduction.