20% = 20/100 = 1/5
That's 1 unit out of 5 units.

So,

Let the selling price of clothing
= ⬛⬛⬛⬛⬛ + $200

After the $200 reduction,
Price = ⬛⬛⬛⬛⬛

After a 20% discount on this price,
Final price = ⬛⬛⬛⬛

Now this price incurs a $50 loss.

So the cost price of the clothing (how much it cost the seller to obtain/procure the clothing)
= ⬛⬛⬛⬛ + $50


Next,

Rearrange the selling price.
Split the $200 into 5 equal parts.
$200 ÷ 5 = $40

It becomes like this :

⬛+$40 ⬛+$40 ⬛+$40 ⬛+$40 ⬛+$40

We get 5 equal parts.


60% = 60/100 = 3/5
That's 3 parts out of 5

So the price after 60% discount means : you have 2 parts left

= ⬛+$40 ⬛+$40
= ⬛⬛+$80

This price is a break-even price.
So it equals the cost price.

Since in the earlier steps the cost price was found to be ⬛⬛⬛⬛ + $50 ,

Then we can say :

⬛⬛⬛⬛ + $50
=
⬛⬛+$80


From this we can compare and realise that :

⬛⬛ = $80 - $50 = $30

⬛ = $30 ÷ 2 = $15


Cost price of clothing
= ⬛⬛⬛⬛ + $50
= $15 × 4 + $50
= $60 + $50
= $110

Or

Cost price of clothing
= ⬛⬛ + $80
= $15 × 2 + $80
= $30 + $80
= $110

Note that when the question says original price, they mean the cost price.

So if you want to earn 100% profit on the clothing,

100% = 100/100 = 1

The profit is 1 time of the cost price. In other words, the profit amount earned is equal to the cost price.

So we have to add $110. (Answer)


This means the price would have to be :
$110 + $110 = $220

Other things you can find :

Selling price = ⬛⬛⬛⬛⬛ + $200
= $15 × 5 + $200
= $75 + $200
= $275


Check :

100% - 60% = 40%
40% = 40/100 = 2/5

If sold at a 60% discount , price would be :

$275 × 2/5 = $55 × 2 = $110 (break even) ✔


If price is reduced by $200,

$275 - $200 = $75

100% - 20% = 80%
80% = 80/100 = 4/5

If this is then sold at 20% discount , price would be :

$75 × 4/5 = $15 × 4 = $60

loss incurred = $110 - $60 = $50 ✔

Wow. Mindblown.

Note that I interpreted 'lose $50' as a loss of $50, and original price as cost price.

There is another interpretation, which would result in a different answer.

If I were to interpret 'lose $50' as 'reduce by $50' and 'original price' as 'original selling price',

Then $50 = 20% of price (after $200 reduction)

100% of price (after $200 reduction)
= $50 × 5
= $250

Original price = $250 + $200 = $450


60% of this = $450 × 3/5 = $270

So this is the 'break-even' price → the cost price of the clothing.


To earn a 100% profit, I need to earn $270.

Price the clothing is to be sold at
= $270 + $270
= $540


Since the original price is $450

Amount to be added to it
= $540 - $450
= $90


I would say the first interpretation is more likely to be correct though.