the altitude at which the weight of a body is only 64%of its weight on the surface of the earth is (

Let m be the mass of the body, g be the acceeleration due to gravity on earth’s surface, G is gravitational constant, M is the mass and R is the radius of the earth, then we know that

Weight of body = Gravitational force between body and earth   ...(1)

i.e. mg = GMm / R²             ...(2)

Let at height h from the earth’s surface, acceleration due to gravity becomes g₁.

Then applying condition (1),  mg₁ = GMm / (R + h)²        ...(3)

Divide (3) by (2) to get mg₁ / mg  =  R² / (R + h)²   or  mg₁ / mg  = 1 / (1 + h/R)²  ..(4)

It is given that mg₁ = 64% of mg  i.e.  mg₁ / mg = 64/100  =  16/25    ..(5)

From (4) and (5),  1 / (1 + h/R)²  =  16/25      (1 + h/R)² = 25/16

1 + h/R  =  5/4      h = R/4.