By selling an umbrella for ? 30, a shopkeeper gains 20%. During a clearance sale, the shopkeeper allows a discount of 10% of the marked price. His gain percentage during the sale season is

Let the CP = N
According to the question, (110N/100) - (80N/100) = 12
? (11N/10) - (4N/5) = 12
? 11N - 8N = 120
? N = 120/3 = 40
? CP = ? 40

Let A purchased the watch for ? N
A x [(1+ r₁) /100] x [(1+ r₂) /100] = CP of article given by C

? N x (140/100) x (80/100) = 432
? N = (432 x 100)/(14 x 8) = ? 385.71

Here, a = 20%
? Total loss percentage = a²/100 %
= (20 x 20)/100
= 4%

Let CP of the article be ? N,
Then 106% of N - 94% of N = 6
? 12% of N = 6
? N = (6 x 100)/12 = ? 50

Required loss = (a/10)²%
= (20/10)²% = 4%
Thus, seller gets 4% loss in the deal.

Let CP = N
Then, according to the question,
(120/100) x (N - 475) = (530 - N)
? (6/5) x (N - 475) = (530 - N)
? (6N - 2850) = (2650 - 5N)
? 11N = 5500
? N = ? 500
? Required SP = (500 x 120)/100 = ? 600

Let required percentage profit = N%
According to the question,
10% of (80 x 50) = 5% of (20 x 50) + N% of (60 x 50)
? (80 x 50 x 10)/100 = [(20 x 50 x 5)/100] + (60 x 50 x N)/100
? 80 = 10 + 6N
? N = 70/6 = 11²/₃%

Required profit = (100 + 65) x (100/120) x (100/125) - 100
= 110 - 100 = 10%

Here, a = 10% , b = 20% , r = 2000
According to the formula
CP of watch = [r/(b - a)] x 100 = [2000/(20 - 10)] x 100
= (2000 x 100)/10
= ? 20000

Loss % = (a/10)²%
= (10/10)²%
= 1%