The weight of an animal varies with its age and height. If the weight of an…
2024
The weight of an animal varies with its age and height. If the weight of an animal is 66 kg when it is 20 years old and 1.1 m in height, then what will be its weight (in kg) when its height is 1.5 m and its age is 22 years?
- A.
99
- B.
100
- C.
94
- D.
90
Attempted by 23 students.
Show answer & explanation
Correct answer: A
CONCEPT: When one quantity varies jointly (directly) with two others, the relationship can be written as Q = k × X × Y, where k is a constant of proportionality found from one known set of values — this is joint variation.
APPLICATION:
Let Weight (W) = k × Age (A) × Height (H), since weight varies jointly with age and height.
Substitute the first data point: 66 = k × 20 × 1.1 = k × 22, so k = 66 ÷ 22 = 3.
Substitute the new age and height into the same relation: W = 3 × 22 × 1.5 = 99 kg.
CROSS-CHECK: Putting k = 3 back into the original data gives 3 × 20 × 1.1 = 66, which matches the given weight — confirming the constant and the joint-variation relation, so the new weight is 99 kg.