Two pans of a balance are 25.1 cm apart.

The fulcrum of the balance has been shifted

1.4 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 %.

25.1%

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 25.1 cm / 2 = 12.55 cm. The fulcrum is then moved 1.4 cm towards the counterweight.

Sum of the moments about the fulcrum:

m (12.55 + 1.4) - M (12.55 - 1.4) = 0

13.95 m - 11.15 M = 0

13.95 m = 11.15 M

M / m = 13.95 / 11.15

M / m = 1.251

The true weight is being marked up by 25.1%.