a particle of mass m moving with speed V collides perfectly inelastically with another particle of mass 2m at rest. fractional loss of kinetic energy of the system in the collision is

during perfectly inelastic collision the two bodies stick after collision and the law of conservation of momentum is valid.

so, from momentum conservation

initial total momentum = final total momentum

mV = (m+2m)V'

where V' is the final velocity of the system

so, we get

V = 3V'

now,

the initial kinetic energy would be

KE = (1/2)mV² = (1/2)m(3V')² 

the final kinetic energy would be

KE' = (1/2)mV'²

thus,

the fractional change in kinetic energy would be

ΔKE / KE = (KE - KE') / KE

or

ΔKE / KE = [(1/2)m(3V')² - (1/2)mV'²] / (1/2)m(3V')²

or

ΔKE / KE = [(3V')² - V'²] / (3V')²

or

ΔKE / KE = 8/9 = 0.88