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# The average weight of 8 persons is increased by 2.5 kg, when one of th

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Math Expert
Joined: 02 Sep 2009
Posts: 58425
The average weight of 8 persons is increased by 2.5 kg, when one of th  [#permalink]

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21 Feb 2019, 00:29
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Difficulty:

15% (low)

Question Stats:

81% (01:26) correct 19% (01:41) wrong based on 43 sessions

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The average weight of 8 persons is increased by 2.5 kg, when one of them whose weight is 56 kg is replaced by a new man. The weight of the new man is :

A. 66 kg
B. 75 kg
C. 76 kg
D. 86 kg
E. 88 kg

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Re: The average weight of 8 persons is increased by 2.5 kg, when one of th  [#permalink]

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21 Feb 2019, 09:59
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Bunuel wrote:
The average weight of 8 persons is increased by 2.5 kg, when one of them whose weight is 56 kg is replaced by a new man. The weight of the new man is :

A. 66 kg
B. 75 kg
C. 76 kg
D. 86 kg
E. 88 kg

sum of 8 = x * 8

so
8x-56+m = (x+2.5)*8
m = 76
IMO C
##### General Discussion
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Re: The average weight of 8 persons is increased by 2.5 kg, when one of th  [#permalink]

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29 Jun 2019, 09:54
There is not a great explanation for the solution of this question so I'll try to clarify:

Average = Sum / Quantity

Let x = Average of original 8 people
Let A = Weight of the new individual
Let (8x+20) = New average (from the prompt)

Therefore:
x = [(sum of 7 original people)+56] / 8

Multiply both sides by 8 and subtract 56 from both sides:
8x-56 = sum of 7 original people

To find the weight of the new person, we must substitute (8x-56) for the sum of the 7 original people in the new average formula:

New Average = [(sum of 7 original people)+A] / 8
(8x+20) = (8x-56)+A

Subtract 8x from both sides and add 56 to both sides:
76=A

The weight of the new person is 76kg.

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Re: The average weight of 8 persons is increased by 2.5 kg, when one of th  [#permalink]

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29 Jun 2019, 15:25
Bunuel wrote:
The average weight of 8 persons is increased by 2.5 kg, when one of them whose weight is 56 kg is replaced by a new man. The weight of the new man is :

A. 66 kg
B. 75 kg
C. 76 kg
D. 86 kg
E. 88 kg

Let the average weight of $$8$$ people be $$= x$$

Weight of one person $$= 56$$ kg

Let the sum of rest $$7$$ person be $$= y$$

Average, $$x = \frac{56 + y}{8} ----- (i)$$

New average is increased by $$2.5 = x + 2.5$$

Let weight of new man be $$= a$$

Average, $$x + 2.5 = \frac{y + a}{8} => x = \frac{y +a}{8} - 2.5 ---- (ii)$$

equating $$(i)$$ and $$(ii)$$;

$$\frac{56 + y}{8} = \frac{y +a}{8} - 2.5$$

$$\frac{56+y}{8} = \frac{y + a- 20}{8}$$

$$56 + y = y+ a - 20$$

$$a = 56 + 20 = 76$$

Age of new man $$= 76$$ kg

Re: The average weight of 8 persons is increased by 2.5 kg, when one of th   [#permalink] 29 Jun 2019, 15:25
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