Question

In a sphere made of an alloy copper and tin are in the ratio 86:14. In a sphere made of another alloy, copper and zinc are in the ratio 58:42. Find the ratio of tin and zinc in the sphere made by melting the two spheres.
A.1:3
B.2:3
C.3:4
D.3:5

Answer 1

Hint: In order to solve the given problem first use the ratio of metals used in both of the alloy of spheres. Convert this ratio in parts and add them to find the parts present in the sphere formed after melting both of them finally find the ratio of the given metals by the help of parts of metals in the final sphere.

Complete step by step answer:
Given that
Ratio of copper and tin in the first alloy is 86:14.
Ratio of copper and zinc in the second alloy is 58:42.
Let us convert them into parts out of the whole.
For first sphere:
Total no of parts $ = 86 + 14 = 100$
We have 86 parts of copper out of 100 parts present.
Also we have 14 parts of tin out of 100 parts present.
For second sphere:
Total no of parts $ = 58 + 42 = 100$
We have 58 parts of copper out of 100 parts present.
Also we have 42 parts of zinc out of 100 parts present.
Now given that both the spheres are melted to form a new sphere.
For the new sphere:
Total no of parts present $ = 100 + 100 = 200$
Parts of copper in this 200 parts is $ = 86 + 58 = 144$
The tin present in 200 parts is 14 parts.
Parts of zinc present in these 200 parts is 42.
Now as we have parts of each metal in the melted sphere, let us find the ratio of tin and zinc.
Ratio of tin and zinc is the same as the ratio of their parts present in the melted sphere.
$ = \dfrac{{14}}{{42}}$
Let us further simplify the ratio.
$ = \dfrac{1}{3}$
Hence, the ratio of tin and zinc in the sphere made by melting the two spheres is 1:3.
So, option A is the correct answer.


Note In order to solve such problems, students must use the formulas related to ratio and proportion. The given problem can also be found out by finding the individual percentage of required metals in both the sphere and then combining it but the method used here is the basic one and is easier to understand. A ratio is a basic mathematical concept which is used to compare two or more quantities expressed in the same units.