WBJEE 2019 Physics Solved Paper

According to the question,
According to Rutherford Soddy law of radioactive decay, the rate of decay of radioactive along at any instant is proportional to the number of atoms present at that instant

dN

dt

=−λN
Since λ = constant (decay constant) and
N = number of atoms
Rate of decay of Y particle is given as
λxNx−λyNy=‌

dNy

dt

=0
[∵ Decay rate for β -particle become constant after some time]
Given, rate of emission of β -particle =107/h
∴λxNx=λYNx=107/h