A dishonest dealer professes to sell his goods at cost price but he uses a weight of 920 g for 1 kg weight. Find his gain per cent

Given that, a = 10% and b = 30%
According to the formula,
Required per cent = [(b - a)/(100 - b)] x 100
= [(30 - 10)/(100 - 30)] x 100
= (20/70) x 100 = 200/7%
= 28⁴/₇% profit

Let the market weight = 1 kg = 1000 g
Real weight = 80% of 1000 = 800 g
Let the CP of 1 g = ? 1
? CP of 800 g = ? 800,
CP of 1000 g = ? 1000
SP = 120% of 1000 = (120/100) x 1000 = ? 1200
Gain = 1200 - 800 = ? 400
? Gain % = (400/800) x 100% = 50%

Here, a = 10% and b = 20%
According to the formula,
Required answer= [b ± a/(100 - b)] x 100 %
= (20 - 10)/(100 - 20 ) x 100%
= (10/80) x 100% = 12.5 % gain
+ ve sign show that profit is earned here.

Here, a = 16, b = 12
According to the formula,
Required gain percent = [(a - b)/b] x 100
= [(16 - 12)/12] x 100
= (4/12) x 100
= 33¹/₃% (gain)

(SP of 100 pens) - (CP of 100 pens) = SP of 40 pens
? SP of 60 pens = CP of 100 pens.

Let CP of each pen = ? 1
Then, CP of 60 pens = ? 60
SP of 60 pens = ? 100

Gain = 100 - 60 = ? 40
? Gain % = (40/60) x 100 % = 66.67%

Given that, a = 4%, b = 28 g and c = 32 g
Required profit = [(100 - a) x (c/b) -100] %
=[(100 - 4) x (32/28) - 100] %
= [96 x (32/28) - 100]%
= [(96 x 8)/7 - 100]%
= (768 - 700)/7 %
= 68/7 %
= 9⁵/₇ % gain
+ ve sign shows that profit is earned here.

Given that, a = 20 and b = 15
According to the formula,
Profit %= [(a - b) / b] x 100 %
= (5/15) x 100% = 100/3 %
= 33¹/₃%

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

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

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