Question on Averages

Question

The average age of Sachin and Ganguli is 35 yrs. If Kaif replaces Sachin, the average age is 32 yrs, if Kaif replaces Ganguly average age is 38 yr. If the average age of Dhoni and Irfan is half of average age of Sachin, Ganguli and Kaif. then average age of all the five people is

A: 28 yrs

B: 32 yrs

C: 25 yrs

D:none of these

Comments

what i want to know is that why it is not giving answer this way.:
 We know that if A+B=l and B+C=k and A+B+C=m
then b = l+K-m.
now i m considering the average age of all 3 to be x.
so taking the two equaltion where ganguaki is common. i can say average age of ganguy = 35+32-x.  similarly  sachin average age 35+38-x . now we have a equation  like  sachin + gangualy = 35. solving i get 51 but it is not what there combined average is. Plz help me .

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Your approach is perfectly fine.
But there is some glitch in your equations for calculating ages of Ganguly & Sachin.
If you are considering A, B, C as actual ages of Ganguly, Sachin & Kaif respectively then
"l" will be 35x2 = 70,
"k" will be 32x2 = 64,

"m" will be 105 (from Equation 4 of my answer).
Also, m is not the average age of all the 3 players, it is the sum of their actual ages.
So try to form equations accordingly.
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Some points about average:
# Average of p & q is (p + q) / 2.
# Average of p is p itself{since p = (p / 1)}.
So here, the average age of Ganguly, will refer to his actual age.
Same for all other players.
# Sum of averages of A, B, & C will not give combined average of A, B & C,
& I guess in your soluion you have assumed m = x, i.e. A + B + C = x.
But the correct equation will be A + B + C = 3x.
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Equations should be like:
Age of Ganguly = (35 * 2) + (32 * 2) - 3x
Age of Sachin = (35 * 2) + (38 * 2) - 3x
Age of Sachin + Age of Ganguly = (35 * 4) + (32 * 2) + (38 * 2) - 6x.
that is, 35 * 2 = (35 * 4) + (32 * 2) + (38 * 2) - 6x.
solving for x, gives x = 35.
Hence the average age of Sachin, Ganguly & Kaif will be 35.
Average player of all the 5 players will be 28.

Answer 1

Option A must be correct.
S : Sachin’s age
G : Ganguly’s age
K : Kaif’s age
D : Dhoni’s age
I : Irfan’s age
Given
(S + G) / 2 = 35
=> ( S + G ) = 70.    Eq 1
(K + G) / = 32
=> (K + G) = 64.    Eq 2
(S + K)/2 = 38
=> (S + K) = 76.    Eq 3
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Eq 1 + Eq 2 + Eq 3 will give:
2(S + G + K) = 210
=> (S + G + K) = 105.        Eq 4
That is the sum ages of S, G & K is 105.
So the average age of S, G & K will be (S + G + K) / 3 = 105 / 3 = 35.
The average age of Irfan & Dhoni = half the average ages of S, G & K.
that is (I + D) / 2 = 35 / 2
=> sum of ages of Irfan & Dhoni i.e. (I + D) = 35    Eq 5
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From Eq 4 & 5, the sum of ages of all the 5 players can be described as follow:
(S + G + K) + (I + D) = 105 + 35 = 140
Hence the average age of all the 5 players = 140 / 5 = 28.

Comments

yes 28 is the ans