Question

A physical balance has pans having weights in the ratio 2:7. An article weighs 27kg when kept on one pan and
43kg when kept on the other. Find the actual weight of the article.​

Answer 1

$pan_{1} : pan_{2} = 2: 7$

let the constant ratios be x

weight of article = y

2x + y = 27

y = 27 - 2x

7x + y = 43

7x + ( 27 - 2x ) = 43   { substituting y with 27 - 2x }

7x + 27 - 2x = 43

7x - 2x + 27 = 43

5x + 27 = 43

5x = 43 - 27

5x = 16

x = 16/5 = 3.2

weight of article = 27 - 2x

=> 27 - ( 2 × 3.2 )

=> 27 - 6.4

=> 20.6 kg

Therefore, the weight of the article is 20.6 kg