Q10 The weight of a body, calculated as the average of seven different experiments is 53.735 g. The average of the first three experiments is 54.005 g. The fourth was greater than the fifth by 0.004 g and the average of sixth and seventh was 0.010 g less than the average of the first three. Find the weight of the body in the third experiment.
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Step-by-step explanation:
i) average of seven exp. = 53.735 g
ii) average of first three exp. = 54.005 g
iii) fourth was greater than the fifth by 0.004 g
iv) average of sixth and seventh was 0.010 g less than the average of the first three
Let the seven different expperiment be x
1
,x
2
,x
3
,x
4
,x
5
,x
6
,x
7
.
i)
7
Σ
i=1
7
x
i
=53.735g
⇒Σ
i=1
7
x
i
=376.145g⟶eq.(1)
ii)
3
Σ
i=1
3
x
i
=54.005g
⇒Σ
i=1
3
x
i
=162.015g⟶eq.(2)
iii) x
4
=x
5
+0.004g
⇒x
5
=x
4
−0.004⟶eq.(3)
iv)
2
x
6
+x
7
=54.005−0.010
⇒x
6
+x
7
=107.99g⟶eq.(4)
From all the above equations we get;
x
1
,x
2
,x
3
,x
4
,x
5
,x
6
,x
7
=376.145g
⇒162.015+x
4
+x
4
−0.004+107.99=376.145
⇒2x
4
=106.144
x
4
=53.072g
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