initially a shopkeeper had n chocolates. a customer bought 10% chocolate from n then another customer bought 20% of the remaining chocolates after that one more customer purchased 25% of the remaining chocolates. finally shopkeeper is left with 270 chocolates in his shop. how many chocolates were there initially in his shop?
Answers
Initially = n chocolates
After customer bought 10%
0.1 x n = 0.1n
n - 0.1n = 0.9n
After customer bought 25% of the remaining
0.25 x 0.9n = 0.225n
0.9n - 0.225n = 0.675n
There were 270 chocolates left
0.675n = 270
n = 270 ÷ 0.675
n = 400
Answer: There were initially 400 chocolates in his shop.
Concept
A value or ratio that may be stated as a fraction of 100 is referred to as a percentage in mathematics. If we need to compute a percentage of a number, we should divide it by its whole and then multiply it by 100. The proportion therefore refers to a component per hundred. Per 100 is what the term percent signifies. The word "percent" is used to symbolize it.
Given
It is given that customer 1 buys 10% chocolates , customer two buys 20% of the remaining chocolates and after that customer 3 buys 25% of the remaining chocolates .
Find
We need to find the initial chocolates
Solution
Let the number n = 1000
From 1000 chocolates Customer 1 buys = 10%
Therefore chocolate bought by the customer is 1000*0.10 = 100
Customer 1 buys = 100 chocolates
The remaining chocolates are 900
Now from 900 customer 2 buys 20% chocolates
Therefore ,
900*0.20 = 180 chocolates
180 chocolates bought by customer 2
Remaining chocolates are 720
25% chocolates bought by customer 3
Therefore ,
720*0.25=180
180 chocolates bought by customer 3
Remaining chocolates are 540
Now we assumed that there are 1000 chocolates total then
540n = 270*1000
Therefore
n = 270/540 *1000
n = 500 chocolates
500 chocolates were initially in his shop
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