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11. A tradesman marks his goods at 25% above the cost price and allows purchasers a discount of 252%, his profit is:

Discuss
Solution:

Let his CP = Rs. 100.
Marked Price = 100 + 25% of 100 = 125.
Now, discount = 252% on MP
So, SP = 125 - 252% of 125 = Rs. 109.375.
%Gain = 9.375%.

Alternatively use graphic change method:
100(CP) == 25% Up ⇒ 125(MP) == 12.5%down ⇒ 109.375
%Profit = 9.375%

12. A bicycle marked at Rs. 2,000, is sold with two successive discount of 20% and 10%.An additional discount of 5% is offered for cash payment. The selling price of the bicycle at cash payment is:

Discuss
Solution:
Marked Price = 2000
SP after first Discount of 20% = 2000 - 20% of 2000 = 1600
SP after second Discount of 10% = 1600 - 10% of 1600 = 1440
Now, the final selling price at cash = 1440 - 5% of 1440 = Rs. 1368

Shortcut by using Graphic Change
2000(MP) == 20%(disc.) ⇒ 1600 == 10%(disc.) ⇒ 1440 == 5%(disc.) ⇒ 1368(SP)
13. The marked price of a shirt and trousers are in the ratio 1:2. The shopkeeper gives 40% discount on the shirt. If the total discount in the set of the shirt and trousers is 30%, the discount offered on the trousers is:

Discuss
Solution:
Let the price of shirt and trouser be Rs. 100 and Rs. 200 respectively.
Then, price of set of shirt and trouser = Rs. 300.
After giving 30% discount on the set,
Selling Price = 300 - 30% of 300 = 210.
Total Discount on Set = 90.
And Discount on shirt is 20% alone,
SP of shirt alone = 100 - 40% of 100 = 60.
Rs. 40 is the discount on shirt then Rs. 50 must be the discount on the trouser.
So, discount on trouser = 50×100200  = 25%.
14. A dealer buys an article marked at Rs. 25,000 with 20% and 5% off. He spends Rs. 1,000 for its repairs and sells it for Rs. 25,000. What is his gain or loss per cent?

Discuss
Solution:
Marked Price = 25000.
After first discount it become,
= 25000 - 20% of 25000 = 20000.
After second discount, it becomes
= 20000 - 5% of 20000 = 19000.
So, SP = 19000.
CP for the man who bought it, as he spends 1000 on repair.
= 19000 + 1000 = 20000
Profit = 25000 - 20000 = 5000.
%Profit = 5000×10020000  = 25%

Short-Cut
25000(MP) == 20%(Disc.) ⇒ 20000 == 5%(disc.) ⇒19000(CP)
Spends on repair = Rs. 1000
Then, CP becomes = 19000 + 1000 = 20000
Profit = 5000
% profit = 5000×10020000  = 25%
15. A trader sells his goods at a discount 20%. He still makes a profit of 25%. If he sells the goods at the marked price only, his profit will be:

Discuss
Solution:
Let the marked price = Rs. 100
Then, SP = 100 - 20% of 100 = Rs. 80
Profit = 25%
Let His CP = X
SP = 80
X + 25% of X = 80
Hence, X = Rs. 100×80125  = Rs. 64
CP = Rs. 64
Profit after selling on marked price = 100 - 64 = Rs. 36
% gain = 36×10064  = 56.25%
16. The marked price of a radio is 20% more than its cost price. If a discount of 10% is given on the marked price, the gain per cent is:

Discuss
Solution:
Let CP = 100
Then, MP = 100 + 20% of 100 = 120
Now, SP = 120 - 10% of 120 = 108
Gain = 108 - 100 = 8
%Gain = 8×100100  = 8%

Short-cut
100(CP) == 20%(up) ⇒ 120(MP) == 10%(disc.) ⇒ 108
% gain = 8%
17. A shopkeeper sells sugar in such a way that the selling price of 950g of sugar is the same s the cost price of 1 kg of sugar. What is his gain percent?

Discuss
Solution:
Sellsugar=950ginsteadof1000gProfitinsugar=1000−950=50gNow,%profit=50×100950=5519%Short - cut:%profit=GoodsleftGoodssold×100=50950×100=5519%
18. After allowing a discount of 11.11%, a trader still makes a gain of 14.28%. At how many percent above the cost price does he mark on his goods?

Discuss
Solution:
Let the CP be Rs. 100, then SP = 100 + 14.28% of 100 = Rs. 114.28
(As Profit = 14.28%)
This profit is arrived after giving discount of 11.11% on the marked price.
Let the marked price be x
X - 11.11% of X = 114.28
X × 100−11.11100  = 114.28
X = 114.28×1008889   = Rs. 128.56, which is more than 28.56% of CP.
19. A dealer buys dry fruits at Rs. 100, Rs. 80, and Rs. 60 per kilogram. He mixes them in the ratio 3:4:5 by weight and sells at a profit of 50%. At what price per kilogram does he sell the dry fruits?

Discuss
Solution:
Let the dealer buys 3 kg, 4 kg and 5 kg.
Price of total dry fruits = 3 × 100 + 4 × 80 + 5 × 60 = Rs. 920
SP = 920 + 50% of 920 = 1380
Hence,
Price of mix dry fruits per kg = 138012 = Rs. 115
20. The cost price of an article is 80% of its marked price for sale. How much per cent does the tradesman gain after allowing a discount of 12%?

Discuss
Solution:
Let the marked price = Rs. 100
Then the cost price = 80% of 100 = Rs. 80
After allowing 12% discount on MP,
SP become = Rs. 88.
% profit = 8×10080  = 10%

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