UPSC CDS 2 2020 Math Paper

We have, the number of items in a booklet =
If first year x% increase in this number.
So, now the number of items in a booklet = N+x% of N
=N+

Nx

100

In subsequent year there is a decrease of x%
So, now the number of items in =(N+

Nx

100

)−x% of (N+

Nx

100

)
=(N+

Nx

100

)−

x

100

(N+

Nx

100

)
=(N+

Nx

100

)(1−

x

100

)
=N(1+

x

100

)(1−

x

100

)
=N(1−

x2

1,00,000

)
So, No. of items is less than N.