The price of an item was increased by 20% and then was reduced by 25% the next day. Which of these can be the new price of the item in Tk if all prices are integer?

Question: The price of an item was increased by 20% and then was reduced by 25% the next day. Which of these can be the new price of the item in Tk if all prices are integer?

Solution:
Let the original price be Tk. p (an integer).
After a 20% increase,
New price = p + p of 20% = p + (20p/100)
= p + (p/5)
= 6p/5

And then reduced by 25%,
Final price = (6p/5) - (6p/5) of 25%
= (6p/5) - (6p/20) = (6p/5) - (3p/10)
= (12p - 3p)/10
= 9p/10
For the final price to be an integer, 9p/10 must be integer and p must be divisible by 10.

Now, check the options,
ক) p = 300 × (10/9) = 333.33 (not integer)
খ) p = 325 × (10/9) = 361.11 (not integer)
গ) p = 450 × (10/9) = 500 (integer)
ঘ) p = 475 × (10/9) = 527.78 (not integer)

Only 450 works as a possible final integer price.
∴ The new price can be Tk 450.