Question

State TRUE or FALSE

If $A:C=5:8$ and $B:C=5:6$, then $A:B$ is $3:4$

• A. True
• B. False

Answer 1

The correct option is A True

In the given ratios "C" is the common term, and the values of C in
both ratios are not equal.

To make them equal, we need to find equivalent ratios of both the ratios such that the values of C are equal.

For this, we need to first find the
L.C.M. of values corresponding to C i.e., $8$ and $6$.
L.C.M. of $8$ and $6=24$

Therefore, an equivalent ratio of $A:C$such that $C=24$, is $A:C=5:8=5\times 3:8\times 3=15:24$

And an equivalent ratio of $B:C$ such that $C=24$, is $B:C=5:6=5\times 4:6\times 4=20:24$

Now the value of C in $15:24$ and in $20:24$
Therefore, $A:B=15:20=3:4$