Question

A bottle weighs 1.2 kg when it is 1/4 full of water. It weighs 2.4 kg when it is full. What is the weight of the empty bottle?

Answer 1

Weight of empty bottle = 0.8 kg

Weight of water = 1.6 kg

Explanation:

As given , A bottle weighs 1.2 kg when it is 1/4 full of water. It weighs 2.4 kg when it is full.

Let us assume

Weight of empty bottle = x

Weight of water = y

Now,

when the bottle is 1/4 full of water

then,

weight of water =
`(1)/(4)`×y

As given , Bottle weight = 1.2 , when it is 1/4 full of water

⇒ Weight of water + weight of bottle = 1.2

⇒
`(1)/(4)`×y + x = 1.2

⇒ y + 4x = 4.8 .......(1)

Also given, A bottle weight = 2.4 , when it is full of water

⇒ Weight of water + weight of bottle = 2.4

⇒ y + x = 2.4 ......(2)

Subtract equation (2) from equation (1) , we get

y + 4x - ( y+ x) = 4.8 - 2.4

⇒ y + 4x - y - x = 2.4

⇒3x = 2.4

⇒x =
`(2.4)/(3)` = 0.8 kg

and y = 2.4 - x = 2.4 - 0.8 = 1.6 kg

∴ we get

Weight of empty bottle = x = 0.8 kg

Weight of water = y = 1.6 kg