Question

A man bought a car 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: In this question, using the percentage formula which if given by \[\dfrac{x}{100}\times y\] we first need to find 10% of 60,000 and then add it to 60,000 which gives the cost price. now, to get the selling price with 15% gain we need to use the profit formula which is given by
\[SP=\dfrac{100+x}{100}\times CP\] and then simplify further to get the result.

Complete step-by-step answer:
As we already know that the percentage formula is given by
\[\dfrac{x}{100}\times y\]
Here we also know that if x% is profit, then we have
\[SP=\dfrac{100+x}{100}\times CP\]
Now, given in the question that a man bought a car for Rs.60,000
Let us now find the amount spent on the tyre which is 10%
Now, on comparing with the percentage formula we have
\[x=10,y=60,000\]
Now, from the percentage formula above we have that
\[\Rightarrow \dfrac{x}{100}\times y\]
Now, on further substituting the respective values we get,
\[\Rightarrow \dfrac{10}{100}\times 60,000\]
Now, on further simplification we get,
\[\Rightarrow 6,000\]
Thus, he spends Rs.6,000 on the tyre
Now, the total cost price is given by the sum of the cost at which he bought the car and the cost he spent on the tyre
\[\Rightarrow CP=60,000+6,000\]
Now, on further simplification we get,
\[\therefore CP=66,000\]
Now, the selling price of the car so that he gets a profit of 15% is given by
\[\Rightarrow SP=\dfrac{100+x}{100}\times CP\]
Now, on comparison we have
\[x=15,CP=66,000\]
Now, on substituting the respective values in the above formula we get,
\[\Rightarrow SP=\dfrac{100+15}{100}\times 66,000\]
Now, this can be further written in the simplified form as
\[\Rightarrow SP=\dfrac{115}{100}\times 66,000\]
Now, on cancelling the common terms and simplifying further we get,
\[\therefore SP=75,900\]

Note: It is important to note that we need to find the amount he spent on the tyre and then need to add that to the price at which he bought because for him to sell the cost price will be the sum of all expenditures on it. if we do not consider that then the result will be incorrect.
It is also to be noted that for him to gain 15% means that he should get a profit of 15% on all cost prices, not on the price at which he bought. We need to substitute all the respective values accordingly and simplify.