Question

If the selling price is doubled, the profit triples. The profit percent is –
(a) 50%
(b) 100%
(c) 120%
(d) None of these

Answer 1

Hint: To solve this problem, we use the formula that profit = selling price – cost price. Here, selling price is the price at which the product is sold after the product is bought at the cost price (as explained, cost price is the price at which a product is bought). Profit percent is given by $\dfrac{\text{Selling Price - Cost Price}}{\text{Cost Price}}\times 100$. We will use this to solve the problem.

Complete step by step answer:
We solve the problem by assuming that the original cost price and selling price be CP and SP. Now, we have the profit (p), we have,
p = SP – CP -- (1)
It is given in the problem that on doubling the selling price, the profit triples, we have,
3p = 2SP – CP -- (2)
Now, we need to find the profit percent given by $\dfrac{\text{Selling Price - Cost Price}}{\text{Cost Price}}\times 100$.
We need to find SP in terms of CP to find the profit percent. We use equations (1) and (2) and solve them to find SP in terms of CP. Firstly, we subtract (1) from (2), we get –
3p-p = SP
SP = 2p -- (A)
Putting this in (1), we get,
p = 2p – CP
CP = p -- (B)
From (A) and (B), we get that SP = 2CP. Now, we put this in the formula of profit percentage given by $\dfrac{\text{Selling Price - Cost Price}}{\text{Cost Price}}\times 100$. We get,
$\left( \dfrac{2CP-CP}{CP} \right)\times 100$ = 100%
Hence, the correct option is (b) 100%.

Note: While solving the equations p = SP – CP and 3p = 2SP – CP (where, p is the profit, SP = selling price and CP = cost price), we see that there are 3 variables for 2 equations. Thus, the equations are explicitly not solvable. However, we are still able to find the required answer since we only have to find the ratio and thus one of the variables cancel out.