Question

Some chocolates are bought at the rate of 11 for ₹ 10 and the same chocolate at the rate of 9 for ₹ 10. If the whole lot is sold at one rupee per chocolate, find the gain or loss per cent on the whole deal.

Answer 1

Hint: In order to solve this problem, we need to assume the number of chocolates but it has to be the multiple of 11 and 9. The easiest way to do that is to take the L.C.M. of 11 and 9. If the cost price is greater than the selling price than the person has suffered a loss and if the selling price is greater than cost price than the person has made a profit. The formula for loss percentage is as follows,
$\text{Loss percentage=}\dfrac{\text{loss}}{\text{cost price}}\text{ }\!\!\times\!\!\text{ 100}$ .

Complete step by step answer:
We have given that some amounts of chocolates are bought at two different rates and they are sold at a single rate.
As we haven’t mentioned anything about the number of chocolates bought we have to assume a number and continue the calculation.
We know the two different rates at which they bought the chocolates. To minimize the complicated calculation, we can take the LCM of the two rates as both are the multiple of that number.
The L.C.M of 11 and 9 is 99. Therefore, let the number of chocolates bought at one particular rate be 99.
We know that the same number of chocolates are bought at different rates. Therefore, the total number of chocolates bought are 99 + 99 = 198.
We have told that the selling price of one chocolate is ₹ 1
Therefore, the selling price of 198 chocolates is = 1 x 198 = ₹ 198.
11 chocolates were bought for ₹ 10, so 99 chocolates were bought for = ₹ $\dfrac{10}{11}\times 99=90$ .
Therefore, the cost price of the first 99 chocolates is ₹ 90.
9 chocolates were bought for ₹ 10, so 99 chocolates were bought for = ₹ $\dfrac{10}{9}\times 99=110$ .
Therefore, the cost price of the last 99 chocolates is ₹ 110.
Therefore, the cost price for 198 chocolates is ₹ 110 + ₹ 90 = ₹ 200
If the cost price is greater than the selling price than the person has suffered a loss and if the selling price is greater than cost price than the person has made a profit.
In this case, the cost price is greater than the selling price, therefore, the person has suffered a loss.
Loss = cost price – selling price
By substituting the values, we get loss – ₹ 200 – ₹ 198 = ₹ 2
Now we need to find the loss percentage. The formula for loss percentage is as follows,
$\text{Loss percentage=}\dfrac{\text{loss}}{\text{cost price}}\text{ }\!\!\times\!\!\text{ 100}$ .
Substituting the values, we get,
Loss percentage = $\dfrac{2}{200}\times 100=1%$.
Therefore, the loss percentage is 1%.

Note: We can have any number of chocolates as long as they are multiple of 11 and 9 because the number of chocolates cannot be a fraction. The only thing that will vary is the loss but the loss percentage will always be the same. This is because the loss percentage is the ratio of two things. We always need to compare the loss or profit at the cost price.