A dishonest dealer purchases goods at 20% discount of the cost price of Rs. x and also cheats his wholesaler by getting 20% extra through false weighing, per kg. Then he marks up his goods by 80% of x, but he gives a discount of 25% besides he cheats his customer by weighing 10% less than the required. What is his overall profit percentage?

Consider actual price of 1 g goods = Re. 1.
He sells the product equals to Rs. 90 only (10% less weighing)
Again MP = Rs.1.8 and SP = 1.35 for 1 g.
Thus he gives the goods worth Rs. 90 and charges Rs. 135 after 25% discount.

Thus the profit % = [(135 - 90) / 90 ] x 100
= 50%

Let the number of the sweets be 100 and the cost price of the one piece of sweet = Re.1
Then, total cost price = 100 x 1 = Rs. 100
Total sale price = (40 x 1.4) + (30 x 1.2) + (30 x 1.05) =123.5
? Profit (%) = 123.5 - 100 = 23.5%

Let the numbers of diaries (produced) be 100 and the cost price of a diary be Rs. 1 then
Total cost incurred = 100 x 1 = 100
Total sale price = 32 x 0.75 + 60 x 1.4 = 108
Therefore profit = Rs. 8
Thus there is 8% profit.

Note : Marked price (i.e. expected) = 40% above the cost price.

You must know that the company is able to deliver only 90% of manufactured pens. So let k be the manufacturing price of a pen, then
Total income (including 25% profit) = 8000 x k x 1.25
Also this same income is obtained by selling 90% manufactured at Rs.10 which is equal to 7200 x 10.
Thus 8000 x K x 1.2 = 7200 x 10
? K = Rs. 7.2 ( 90% of 8000 = 7200)

From question, Chaudhary's profit = 10%.
So, Anupam's profit = 20%
Bhargava profit = 25%

Now Let cost price for Anupam = Rs. 100
So cost price for Bhargava = 120
Cost price for Chaudhary = 150
Cost price for Dara Singh = 165

Since the cost price for Dara singh is 2805 which is 17 times of 165. So the cost price for Bhargava is 120 x 17 = Rs. 2040.

Given,
CP of p apples = q
? CP of 1 apple = q/p
and SP of q apples = p
? SP of 1 apple = p/q

Given, p < q
? Loss = q/p - p/q = (q² - p²) / pq
And Loss% = (Loss/CP) x 100
= {(q² - p²)/pq} /(q/p)] x 100
= (q² - p²)/q² x 100

Therefore, when p < q , then the person had a loos which is given by
100 x (q² - p²/q²)% loss.

Let CP = ? 100
Then, SP = ? 140
Let the profit made by the 2nd dealer = N%
Then, (100 + N)% of 120% of ? 100 = ? 140
? [(100 + N)/100 x (120/100) ] / 100 = 140
? 6(100 + N) = 700
? 600 + 6N = 700
? 6N = 100
? N = (100/6)% = (50/3) %
= 16²/₃

Let cost price of a wall clock = ? N
? Cost price of a watch = ? (390 - N)
According to the question,
{(N x 10)/100} + {(390 - N) x 15}/100 = 51.50
? 390 x 15 - 5N = 51.50 x 100
? 5N = 5850 - 5150 = 700
? N = 700/5 = 140

? Required difference = (390 - N) - N
= 390 - (2 x 140)
= 390 - 280 = 110
= ? 110

Let the sugar sold at 8% gain = P
? Sugar sold at 18% gain = (1000 - P)
Let CP of sugar = ? Q per kg
Total CP = ? 1000 x Q
? [(108/100) x PQ)] + [(118/100) x (1000 - P) x Q]
= (114/100) x 1000 Q
? 108PQ + 118000Q - 118PQ = 114000Q
? 10P = 4000
? P = 400
? Quantity sold at 18% profit = 1000 - 400 = 600 kg

Total CP = (95% of 80% of ? 25000) + (2000)
= (95/100) x (80/100) x 25000 + 2000
= 19000 + 2000 = ? 21000
? CP = ? 21000 and SP = ? 25000
? Gain = 25000 - 21000 = ? 4000
? Gain % = (4000/21000) x 100% = 400/21%
= 19.05% (approx.)