The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity. Which of these may be 50% of the weight of the bucket when it is filled with water (assume the weight of bucket and its capacity in kg to be integers)?
Answers
Answer:
Step-by-step explanation:
W=weight of bucket
V=volume of bucket
W + 0,5V = 1,33W
so 0,5V = 0,33W
it wants us (W+V)/2 that is (W + 0,66W)/2= 0,83W But we do not know anything else. So anyone can be. But the sentence in paranthesis gives us a clue. Capacity of bucket and weight of bucket are integer. So W and 0,66W is integer. i.e. W and 2/3W is integer. So we can assume that W is a multiple of 3 (say 3n) . And 0,66 W is a multiple of 2 (say 2n). So they make a multiple of 5 together (3n+2n).
So the answer, IMO, 3.
GIven : The weight of an iron bucket increases by 33.33% when filled with water to 50% of its capacity A. 7Kg , B. 6Kg , C. 5kg , D. 8kg
To find : 50% of the weight of the bucket when it is filled with water
Solution:
The weight of an iron bucket = 3W kg
Capacity of Bucket = 2V kg
filled with water to 50% of its capacity = (50/100)2V = V kg
The weight of an iron bucket increases by 33.33%
=> (33.33/100)3W = W kg
=> W kg = V kg
Let say W = V = n ( integer)
then 2V = 2n ( capacity)
Weight of bucket = 3W = 3n ( weight)
50% of the weight of the bucket when it is filled with water
= (50/100) ( 3W + 2V)
= (1/2) (3n + 2n)
= 5n/2
Hence Weight would be a multiple of 5
Hence 5 kg is the correct answer
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