Some chocolates are bought at the rate of 11 for 10 Rs and the same number at the rate of 9 for 10 Rs. If the whole lot is sold at one rupee per chocolate, find the gain or loss percent on the whole dealing. ( Hint: let the number of chocolates bought be LCM of 11 and 9.)

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## Answers & Comments

## The loss percent of overall dealing is 1 %

Solution:Given that let the number of chocolates bought be LCM of 11 and 9

L.C.M of 11 and 9:List all prime factors for each number

Prime Factorization of 9 is:

Prime Factorization of 11 is:

For each prime factor, find where it occurs most often as a factor and write it that many times in a new list.

The new superset list is

3, 3, 11

Multiply these factors together to find the LCM.

LCM = 3 x 3 x 11 = 99

So the total number of chocolates bought = 99 + 99 = 198Given that whole lot is sold at one rupee per chocolate

So, Selling price of 1 chocolate = Rs 1

Therefore, S.P of 198 chocolates = 1 x 198 = Rs 198

Given that Some chocolates are bought at the rate of 11 for 10 RsSo cost price of 99 chocolate at rate of 11 of Rs 10

Given that same number at the rate of 9 for 10 RsSo cost price of 99 chocolate at rate of 9 of Rs 11

Therefore C.P of all 198 chocolates = Rs 90 + Rs 110 = Rs 200

On comparing cost price and selling price, we get

cost price > selling price , which denotes lossLet us calculate the loss

Loss = Cost price - selling price

Loss = Rs 200 - Rs 198 = Rs 2

Therefore loss = 2Therefore

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