A cuboidal water purifier can carry 10 liters of water. Its breadth is of its height and length of the sum of the breadth and height. The height of the tank is:
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 50 cm.
We know,
Length = l
Width = b
Height = h
Breadth = 1/5 of height
⇒ B = 1/5 × h
Length = 1/3 × (Breadth + Height)
1 litre = 1000 cm3
Volume of the purifier = 10 × 1000 = 10000 cm3
⇒ l × b × h = 10000
Now,
Length in terms of height:
⇒ l = 1/3(h/5 + h)
⇒ l = 2h/5
Putting the values of l, b, and h
⇒ h × h/5 × 2h/5 = 10000
⇒ 2h3/25 = 10000
⇒ 2h3 = 250000
⇒ h3 = 125000
⇒ h = 50
Hence, The height of the tank is 50 cm.