QUESTION 11 There were 100 chocolates in a box. The box was passed down
along a row of people.
The first person took one chocolate. Each person down the row took more
chocolates than the person before, until the box was empty.
What is the largest number of people that could have been in the row?
Answers
Answer:
chocolates taken-
1,2,3..... n
total chocolates = 100
sum of n numbers = 100
n= ?
sum of n numbers = n(n+1)/2
100 = n(n+1)/2
by cross multiplication
200 = n(n+1)
200 = n²+n
n²+n-200 = 0
formula for finding solution of quadratic equation=
y :
- B ± √ B²-4AC
n = ————————
2A
In our case, A = 1
B = 1
C = -200
Accordingly, B2 - 4AC =
1 - (-800) =
801
Applying the quadratic formula :
-1 ± √ 801
n = ——————
2
Two real solutions:
n =(-1+√801)/2=(-1+3√ 89 )/2= 13.651
or:
n =(-1-√801)/2=(-1-3√ 89 )/2= -14.651
Two solutions were found :
n =(-1-√801)/2=(-1-3√ 89 )/2= -14.651
n =(-1+√801)/2=(-1+3√ 89 )/2= 13.651
people can never be negative.
so there are 13 people.
1+2+3+..+13 = 91
so the answer is approx.