UPSC CAPF Assistant Commandant Model Paper 2

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.