GIVEN: Melted weight of chain and ring is 20 grams and 25 grams respectively. Chain and ring are 90% and 80% pure while new ornament is 76% pure. CONCEPT: Mixture FORMULA USED: No formula CALCULATION: Let purity of new ornament before adding impurity be X% By the rule of allegation
So, 80 – X) : (X – 90) = 20 : 25 = 4 : 5 ⇒ 400 – 5X = 4X – 360 ⇒ X = 760/9% Pure gold = 760/9% of 45 = 38 grams Impurity = 45 – 38 = 7 grams Let added impurity be p Now, 38 = 76% of (45 + p) ⇒ 50 = 45 + p ⇒ p = 5 ∴ Extra added impurity by goldsmith is 5 grams.