Question

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. 

(a) 52.071 g

(b) 53.072g

(c) 51.450 g

(d) 53.005 g

Answer 1

Correct option is (b) 53.072g

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 experiment be x₁​, x₂​, x₃​, x₄​, x₅​, x₆​, x₇​.

From all the above equations we get;

 x₁​, x₂​, x₃​, x₄​, x₅​, x₆​, x₇​ = 376.145g

⇒ 162.015 + x₄ ​+ x_4​ − 0.004 + 107.99 = 376.145

⇒ 2x₄​ = 106.144

⇒ x₄​ = 53.072g