Question

Two pans of a balance are 65.3 cm apart.

The fulcrum of the balance has been shifted
1.48 cm away from the center by a dishonest
shopkeeper.
By what percentage is the true weight of the
goods being marked up by the shopkeeper?
Assume the balance has negligible mass.
Answer in units of %.

Answer 1

9.50%

Step-by-step explanation:

Let's say m is the true weight and M is the weight of the counterweight.

The original distance between the pans and the center is 65.3 cm / 2 = 32.65 cm. The fulcrum is then moved 1.48 cm towards the counterweight.

Sum of the moments about the fulcrum:

m (32.65 + 1.48) − M (32.65 − 1.48) = 0

34.13 m − 31.17 M = 0

34.13 m = 31.17 M

M / m = 34.13 / 31.17

M / m = 1.0950

The true weight is being marked up by 9.50%.