Question

the weight of the bucket is 15 kg when it filled upto 2/5 of its capacity and the weight is 19 kg. when it filled 4/5​

Answer 1

$\bf\large\underline\red{Solution:-}$

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The weight of bucket when filled with water is actually the weight of the bucket and the weight of the water together. In both 3/5 and 4/5 cases weight of the bucket is constant, let it be x. 

Weight wen filed till 3/5: x+ weight of 3 parts ( each part 1/5 of the total capacity) of water. Let that be x+3y. It is 15kg. 

Similarly in the 4/5 case, the equation would be x+4y=19kg. 

Now, to the solving part, 

x+3y=15 

x= 15-3y. 

Now substitute this in the second equation, 

x+4y= 15-3y+4y=19. 

15+y=19. 

y= 4. 

That is, one part of water weighs 4kg. Similarly frm the equation you'll get x, the weight of the bucket to be 3kg. 

Now when filled to capacity the weight will be weight of the bucket and weight of five parts (full is5/5) of water: 3+4*5=23.

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Answer 2

$\huge\purple{Answer:-}$

The weight of bucket when filled with water is actually the weight of the bucket and the weight of the water together. In both 3/5 and 4/5 cases weight of the bucket is constant, let it be x.

Weight wen filed till 3/5: x+ weight of 3 parts ( each part 1/5 of the total capacity) of water. Let that be x+3y. It is 15kg.

Similarly in the 4/5 case, the equation would be x+4y=19kg.

Now, to the solving part,

x+3y=15

x= 15-3y.

Now substitute this in the second equation,

x+4y= 15-3y+4y=19.

15+y=19.

y= 4.

That is, one part of water weighs 4kg. Similarly frm the equation you'll get x, the weight of the bucket to be 3kg.

Now when filled to capacity the weight will be weight of the bucket and weight of five parts (full is5/5) of water: 3+4*5=23.