Question

Two pans of a balance are 24.1 cm apart. The fulcrum of the balance has been shifted 1.33 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

As we know that fulcrum is shifted to one side by 1.33 cm

so here let say left side mass is m1 while on other side mass is m2

so we will have

$m_1g (24.1 - 1.33) = m_2 g(24.1 + 1.33)$

$m_2 = 0.895 m_1$

now in order to find the percentage we have

$percentage = \frac{m_1 - m_2}{m_1}\times 100$

$percentage = (1 - 0.895)\times 100$

$percentage = 10.5%$

so it is 10.5 % less mass