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P and Q are two alloys which are prepared by mixing tin and lead in the ratio of 12 : 5 and 4 : 3 respectively. If equal quantities of alloys are melted to form a third alloy R, then what is the ratio of tin and lead in alloy R?

P and Q are two alloys which are prepared by mixing tin and lead in the ratio of 12 : 5 and 4 : 3 respectively. If equal quantities of alloys are melted to form a third alloy R, then what is the ratio of tin and lead in alloy R? Correct Answer 76 : 43

Let ‘x’ units of P and Q alloys are melted to form third alloy

Tin-lead ratio in P alloy = 12 ∶ 5

⇒ Quantity of Tin in ‘x’ units of P alloy = (12/17)x

⇒ Quantity of Lead in ‘x’ units of P alloy = (5/17)x

Similarly,

Tin-lead ratio in Q alloy = 4 ∶ 3

⇒ Quantity of Tin in ‘x’ units of Q alloy = (4/7)x

⇒ Quantity of Lead in ‘x’ units of Q alloy = (3/7)x

Hence,

Total quantity of Tin in R alloy = (12/17)x + (4/7)x = (152/119)x

Total quantity of Lead in R alloy = (5/17)x + (3/7)x = (86/119)x

∴ Tin-lead ratio in R alloy = (152x/119) ∶ (86x/119) = 152 ∶ 86 = 76 ∶ 43

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