1) The average age of a group of people going for picnic is 16 years. 20 new people with an average age of 15 years join the group on the spot due to which their average becomes 15.5, Find the no. of people initially in the group going for the picnic.
options= 1) 20 , 2) 18, 3) 22, 4) None of these

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Solution

Let x= number of people initially going for picnic.
Given
average age of x people = 16
$\frac{S u m_{1}}{x} = 16 s u m_{1} = 16 x . . (1) A f t e r 20 p e o p l e j p i n e d, a v e r a g e = 15 \frac{s u m_{2}}{20} = 15 s u m_{2} = 300 T o t a l a v e r a g e = 15.5 \frac{s u m_{1} + s u m_{2}}{x + 20} = 15.5 \frac{16 x + 300}{x + 20} = 15.5 (f r o m (1) a n d (2)) 16 x + 300 = 15.5 (x + 20) 16 x + 300 = 15.5 x + 310 0.5 x = 10 x = \frac{10}{0.5} = 20$

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1) The average age of a group of people going for picnic is 16 years. 20 new people with an average age of 15 years join the group on the spot due to which their average becomes 15.5, Find the no. of people initially in the group going for the picnic.options= 1) 20 , 2) 18, 3) 22, 4) None of these

Let x= number of people initially going for picnic. Given average age of x people = 16 Sum1x=16sum1=16x ..(1)After 20 people jpined,average = 15 sum220=15sum2=300Total average = 15.5sum1+sum2x+20=15.516x+300x+20=15.5(from (1) and (2))16x+300=15.5(x+20)16x+300=15.5x+3100.5x=10x=100.5=20

1) The average age of a group of people going for picnic is 16 years. 20 new people with an average age of 15 years join the group on the spot due to which their average becomes 15.5, Find the no. of people initially in the group going for the picnic.
options= 1) 20 , 2) 18, 3) 22, 4) None of these