Given below are two statements: Statement I: Sometimes, Ratio has units.…
2020
Given below are two statements:
Statement I: Sometimes, Ratio has units.
Statement II: When two ratios are equal, a proportion is formed.
In the light of the above statements, choose the correct answer from the options given below:
- A.
Both Statement I and Statement II are true
- B.
Both Statement I and Statement II are false
- C.
Statement I is correct but Statement II is false
- D.
Statement I is incorrect but Statement II is true
Attempted by 7 students.
Show answer & explanation
Correct answer: D
Concept
A ratio compares two quantities of the SAME kind by division (a : b = a/b). Because both quantities are measured in the same unit, those units cancel, so a pure ratio is a dimensionless (unit-less) number. A proportion is the statement that two such ratios are equal: a : b = c : d, i.e. a/b = c/d.
Application
Evaluate each statement against these definitions:
Statement I claims a ratio sometimes has units. Since a ratio compares same-kind quantities, the units always cancel and the result is a bare number (e.g. 6 cm : 2 cm = 3, no unit). Hence a ratio carries NO units, and Statement I is FALSE.
Statement II says that when two ratios are equal a proportion is formed. This is exactly the definition of a proportion (a/b = c/d). Hence Statement II is TRUE.
So Statement I is incorrect and Statement II is correct.
Cross-check
Check II with numbers: 2 : 4 and 3 : 6 both equal 1/2, so 2 : 4 :: 3 : 6 is a valid proportion — confirming II. For I, even mixed-looking cases (like speed) are rates, not ratios in the strict same-kind sense, so a true ratio stays unit-less. Result: Statement I incorrect, Statement II true.