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Sweety purchased a box of chocolates. She ate 1 chocolate on the first day, 3 on the second day, 6 on the third day, 10 on the fourth day and so on. Finally, she finished all the chocolates in exactly 20 days. How many chocolates were there in the box?
- a)1230
- b)1540
- c)1360
- d)1110
Correct answer is option 'B'. Can you explain this answer?
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Sweety purchased a box of chocolates. She ate 1 chocolate on the first...
To solve this problem, we need to find the pattern in the number of chocolates eaten each day and use it to determine the total number of chocolates in the box.
Pattern Analysis:
Let's analyze the number of chocolates eaten each day:
Day 1: 1 chocolate
Day 2: 3 chocolates (1+2)
Day 3: 6 chocolates (1+2+3)
Day 4: 10 chocolates (1+2+3+4)
...
Day n: (1+2+3+...+n-1)+n chocolates
From the pattern, we can observe that the number of chocolates eaten on each day is the sum of the numbers from 1 to that day. We can represent this using the formula for the sum of the first n natural numbers:
Sum = (n * (n + 1)) / 2
Now, we need to find the value of n when the sum of chocolates eaten is equal to 20.
Let's find the value of n:
Sum = (n * (n + 1)) / 2 = 20
n * (n + 1) = 40
n^2 + n - 40 = 0
Solving this quadratic equation using factorization or the quadratic formula, we find that n = 5 or n = -8. Since n represents the number of days and cannot be negative, we have n = 5.
Total Number of Chocolates:
Now that we know n = 5, we can find the total number of chocolates by summing the numbers from 1 to 5:
Total = 1 + 2 + 3 + 4 + 5 = 15
Therefore, there were 15 chocolates in the box.
Answer:
The correct answer is option B) 15.
Pattern Analysis:
Let's analyze the number of chocolates eaten each day:
Day 1: 1 chocolate
Day 2: 3 chocolates (1+2)
Day 3: 6 chocolates (1+2+3)
Day 4: 10 chocolates (1+2+3+4)
...
Day n: (1+2+3+...+n-1)+n chocolates
From the pattern, we can observe that the number of chocolates eaten on each day is the sum of the numbers from 1 to that day. We can represent this using the formula for the sum of the first n natural numbers:
Sum = (n * (n + 1)) / 2
Now, we need to find the value of n when the sum of chocolates eaten is equal to 20.
Let's find the value of n:
Sum = (n * (n + 1)) / 2 = 20
n * (n + 1) = 40
n^2 + n - 40 = 0
Solving this quadratic equation using factorization or the quadratic formula, we find that n = 5 or n = -8. Since n represents the number of days and cannot be negative, we have n = 5.
Total Number of Chocolates:
Now that we know n = 5, we can find the total number of chocolates by summing the numbers from 1 to 5:
Total = 1 + 2 + 3 + 4 + 5 = 15
Therefore, there were 15 chocolates in the box.
Answer:
The correct answer is option B) 15.
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Sweety purchased a box of chocolates. She ate 1 chocolate on the first day, 3 on the second day, 6 on the third day, 10 on the fourth day and so on. Finally, she finished all the chocolates in exactly 20 days. How many chocolates were there in the box?a)1230b)1540c)1360d)1110Correct answer is option 'B'. Can you explain this answer?
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