some chocolate are bought at the rate of 11 for ₹10 and the same number at the rate of 9 for ₹10. If the whole lot is sold at one rupee per chocolate, find the gain or loss per percent on the whole dealing. [ Hint:Let the number of chocolates bought be LCM of 11 and 9 .]
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Answers
Answer:
11 chocolates were bought for ₹ 10, so 99 chocolates were bought for = ₹ 1011×99=90 . Therefore, the cost price of the first 99 chocolates is ₹ 90. 9 chocolates were bought for ₹ 10, so 99 chocolates were bought for = ₹ 109×99=110 .
Answer:
Step-by-step explanation:
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 = ₹ 1011×99=90 .
Therefore, the cost price of the first 99 chocolates is ₹ 90.
9 chocolates were bought for ₹ 10, so 99 chocolates were bought for = ₹ 109×99=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,
Loss percentage=losscost price × 100 .
Substituting the values, we get,
Loss percentage = 2200×100=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.