Question

An alloy of Copper and tin weights 176 kg. the ratio of the weight of copper to that of tin in the alloy is 5:6 .find the weights of copper and tin in the alloy. ​

Answer 1

${\bf{\underline{\underline{Concept \: \: of \: the \: question : }}}}$

Here Question says that Total weight to Alloy of Copper and tin is 176 kg and ratio of their weight is 5 : 6. We need to find Weight of Copper and as well as tin in the alloy. So, at first we we will assume ratio in x form and then we will find value of x by equating them. By putting the value of x in unknown value, it will give weights of copper and tin in the alloy.

${\bf{\underline{\underline{Assumption : }}}}$

• Let Ratio be in x form as 5x and 6x.

${\bf{\underline{\underline{Given : }}}}$

• Alloy of Copper and tin weights 176 kg.
• Ratio of their Weight is 5 : 6 .

${\bf{\underline{\underline{To \: \: find : }}}}$

• Weights of copper and tin in the alloy.

${\bf{\underline{\underline{Solution \:with \: Explanation : }}}}$

● We have

• 5x & 6x
• 176

● Making the equation

${\large{\bf{\implies{5x + 6x = 176}}}}$

● Value of x is

${\bf{\implies{5x + 6x = 176}}}$

${\bf{\implies{11x = 176}}}$

${\bf{\implies{x = \cfrac{176}{11} }}}$

${\bf{\implies{x = 16}}}$

_______________________________________

○ Weight of the Copper is :-

⇒ 5x

⇒ 5 × 16

⇒ 80 kg

○ Weight of the Tin is :-

⇒ 6x

⇒ 6 × 16

⇒ 96 kg

___________________________

VERIFICATION

⇒ Weight of the Tin + Weight of the Copper = 176

⇒ 96 + 80 = 176

⇒ 176 = 176

LHS = RHS

Hence value of x is correct and Weight of the Tin , Weight of the Copper is correct.