A's weight is 25% of B's weight and 40% of C's weight. What percentage of C's…
2023
A's weight is 25% of B's weight and 40% of C's weight. What percentage of C's weight is B's weight?
Answer: A. 160 — ConceptWhen the same quantity is expressed as p% of X and q% of Y, pX/100 = qY/100, so X/Y = q/p. To express X as a percentage of Y, first find X/Y and then…
- A.
160
- B.
180
- C.
150
- D.
More than one of the above
- E.
None of the above
Attempted by 3 students.
Show answer & explanation
Correct answer: A
Concept
When the same quantity is expressed as p% of X and q% of Y, pX/100 = qY/100, so X/Y = q/p.
To express X as a percentage of Y, first find X/Y and then multiply that ratio by 100.
Application
Let A, B, and C denote the three weights.
From the statements, A = 25B/100 = B/4 and A = 40C/100 = 2C/5.
Equating the two expressions for A gives B/4 = 2C/5.
Multiplying by 20 gives 5B = 8C, hence B/C = 8/5 = 1.6.
Therefore, B as a percentage of C is 1.6 × 100 = 160%.
Cross-check
Take A = 10. Then B = 40 and C = 25; 25% of 40 and 40% of 25 are both 10, while 40/25 = 1.6.
Result: B is 160% of C.