Question

A man bought a car of Rs.$60,000$ and spent $10\% $ of the cost of the car for the purchase of the new tyre. At what price should he sell the car to make a gain of $15\% $?

Answer 1

Hint: First find the total cost by adding the cost price of the car and the cost price of the new tyre. Then use the formula - S.P. =$\dfrac{{100 + {\text{gain% }}}}{{100}} \times {\text{C}}{\text{.P}}{\text{.}}$ where C.P. is total cost price, to find the value of selling price of the car.

Complete step by step answer:

Given the cost price of the car= Rs.$60,000$
And the cost price of the new tyre=$10\% $ of the cost of the car
We have to find the selling price which gains the man profit of $15\% $
Here the cost of the new tyre will be=$\dfrac{{10}}{{100}} \times 60,000$
On solving we get,
The cost price of the new tyre=$6000$
Then the total cost price =cost price of the car +cost price of the tyre
On putting the values we get,
Total cost price=$60,000 + 6000 = 66000$
When cost price and gain% is given then we use the following formula to find the selling price-
S.P. =$\dfrac{{100 + {\text{gain% }}}}{{100}} \times {\text{C}}{\text{.P}}{\text{.}}$
On putting the values in the formula we get,
S.P. =$\left( {\dfrac{{100 + 15}}{{100}}} \right) \times 66000$
On solving the values inside the bracket we get,
S.P. =$\dfrac{{115}}{{100}} \times 66000$
Om multiplication we get,
S.P. =$\dfrac{{7590000}}{{100}}$
On division we get,
S.P. =$75900$
Answer- The man should sell the car at Rs. $75900$to make a gain of$15\% $.

Note: Here we can also solve this question by first finding the profit by using formula-
Profit=$\dfrac{{C.P. \times {\text{Profit}}\% }}{{100}}$
On putting the given values we get,
Profit=$\dfrac{{66000 \times 15}}{{100}} = 9900$
Now we can find the selling price by using formula-
S.P. =Profit +C.P.
On putting the values in the formula we get,
S.P. =$9900 + 66000 = 75900$