Question

A hill, `101 1/3` m in height, has `1/4` th of its height under water. What is the height of the hill visible above the water?

Answer 1

Given, height of the hill = `101 1/3` m

= `((101 xx 3) + 1)/3`

= `(303 + 1)/3`

= `304/3` m

∵ Height of the hill under after = `1/4` of the height of the hill

= `1/4 xx 304/3`

= `76/3` m

∴ Height of the hill above the water = Height of the hill – Height of the hill under water

= `304/3 - 76/3`

= `228/3`

= 76 cm

Hence, height of the hill above the water is 76 cm.

Alternate Method: Fraction of height of the hill above water = `1 - 1/4`

= `(4 - 1)/4`

= `3/4`

So, `3/4` of the height of the hill is visible.

∴ Height of the hill above the water = `3/4` × Height of the hill

= `3/4 xx 101 1/3`

= `3/4 xx ((101 xx 3) + 1)/3`

= `3/4 xx 304/3`

= 76 m