Question

Assertion (A): If $$2x = 3y$$ and $$4y = 5z$$, then $$x : y : z$$ is equal to $$15 : 10 : 8$$.

Reason (R): If $$x = y$$ and $$y = z$$, then we cannot find the ratio $$x : y : z$$.

पर्याय

• Both A and R are true, and R is the correct explanation of A.

• Both A and R are true, but R is not the correct explanation of A.

• A is true, but R is false.

• A is false, but R is true.

Answer 1

A is true, but R is false.

Explanation:

Step 1 – Assertion: A is true. From $$2x=3y$$, $$x:y=3:2$$; from $$4y=5z$$, $$y:z=5:4$$. Matching the common term gives $$x:y:z=15:10:8$$.

Step 2 – Reason: R is false. If $$x=y$$ and $$y=z$$, then $$x=y=z$$, so the ratio is $$x:y:z=1:1:1$$.