A shopkeeper fixes the marked price of a pair of shoes $45$ % above its cost price. What is the percentage of discount allowed to gain $16$ %?

Given:

Marked price of a pair of shoes $=45$ % above its cost price.

To do:

We have to find the percentage of discount allowed to gain $16$%.

Solution:

Let the cost price be $Rs.\ 100$

This implies,

Marked price $=Rs.\ (100+45)=Rs.\ 145$

Required gain $=16 \%$.
This implies,

Selling price S.P $= Rs. (100+16)$

$=Rs.\ 116$

We know that,

Discount $ \% = \frac{(MP – SP)}{MP} \times 100$

Discount $=MP - SP$

$= Rs.\ 145-Rs.\ 116 = Rs.\ 29$

Discount % $= \frac{29}{145}\times 100 \%$

$= 20 \%$