Question 122

The average of 18 numbers is 52. The average of the first 8 numbers is 62 and the average of the next 7 numbers is 45. If the $$16^{th}$$ number is 6 less than the $$17^{th}$$ number and the $$17^{th}$$ number is one more than the $$18^{th}$$ number. then what is the average of the $$16^{th}$$ and $$18^{th}$$ numbers ?

Solution

sum of 16 no. =$$18\times\ 52=936$$

sum of first 7 no. =$$8\times\ 62=496$$

sum of next 6 no. =$$7\times\ 45=315$$

remaining sum=$$936\ -\ \left(496+315\right)=125$$

i.e 18th+17th+16th=125

ATQ

let 16th no. =x-6

threfore 17th=x-1

and 18th =x

now,x+x+1+x-6=125

3x-5=125

x=43

16th no = 38,17th no = 44, 18th no =43

average of 16th and 18th =

average=40.5 Ans

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