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71. A man purchased the articles for Rs. 123684. He sold 60% of those at a profit of 16.66% and rest at a loss. Find the loss percentage on the remaining if the overall loss is 14%?

Discuss
Solution:
He gets 14% of loss that means he gets 86% of CP.
Thus,
Let the CP be Rs. 100
60% of 100 + 16.66% of 60% of 100 + 40% of 100 - x% of 40% of 100 = 86% of 100
70 + 40X = 86
40X = 86 - 70 = 16
X = 1640
X = 0.4
Hence, Loss = 1 - 0.4 = 0.6 = 60%
72. A reduction of 20% in the price of sugar enables a housewife to purchase 6 kg more for Rs. 240. What is original price per kg of sugar.

Discuss
Solution:
It is based on inverse proportion or product constancy concept. Reduction in price 20% amount of sugar will increase 25%
It means,
25% = 6 Kg. So,
Initially, total Sugar = 6 × 4 = 24Kg. Thus,
Original price of the sugar was,
24024 = Rs. 10 per kg.

Note:
Let initial price of 100 kg Sugar was Rs. 100.
Now, 20% decrease in rate then rate of 100 kg sugar would be Rs. 80.
So,
Rs. 80 = 100 kg sugar.
Rs. 1 = 10080 kg sugar.
Rs. 100 = 100×10080   = 125 Kg sugar.
Increment in sugar = 25 kg.
% increment = 25×100100   = 25%.
Means 20% rate decrease, 25% of consumption increase.
73. 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?

Discuss
Solution:
Let actual cost price of an article be Rs. 1 (in place of X). Now he purchases goods worth Rs. 120 and pays Rs. 80, since 20% discount is allowed.
So, the CP = 80120=23
Again, MP, SP = 135 (since 25% discount)
Thus, the trader sells goods worth Rs. 90 instead of 100g and charges Rs. 135.
Therefore the effective SP = 13590=32
Profit%=32−2323×100=125%
74. Hotel Aditya has 10 single AC rooms, 5 double AC rooms and 18 non AC rooms. The fixed monthly rent of hotel is 150,000. The per day maintenance cost is Rs. 100 for double AC room, Rs. 75 for single AC room and Rs. 40 for non AC room. The per day charges are Rs. 600 for double AC room, Rs. 400 for single AC room and Rs. 250 for non AC room. In April 2003, the occupancy rate of non AC room was 50%, 70% of single AC room and 40% of double AC rooms. Find the profit/loss % for that particular month.

Discuss
Solution:
Maintenance,
= Rs. (100 × 5 × 30) + (75 × 10 × 30) + (40 × 18 × 30)
= 15,000 + 22,500 + 21,600
= Rs. 59,100

Total cost = 2,09,100
Amount Received,
= (9 × 250 × 30) + (7 × 400 × 30) + (2 × 600 × 30)
= 67,500 + 84,000 + 36,000
= 1, 87, 500

Loss (%),
=209100−187500209100×100=21600209100×100=10.33%
75. A bookseller procures 40 books for Rs. 3200 and sells them at a profit equal to the selling price of 8 books. What is the selling price of one dozen books, if the price of each book is same?

Discuss
Solution:
Cost price of each book,
= 320040  = Rs. 80.
Now,
Selling Price of 40 books = CP of 40 books + SP of 8 books.
Selling Price of 40 books - SP of 8 books = CP of 40 books.
SP of 32 books = Rs. 3200
SP of 1 book = 320032  = Rs. 100.
So, Selling price of one dozen (12) book = 12 × 100 = Rs. 1200
76. A style cloth emporium the shopkeeper measures 20% less for every metre of cloth also he marks-up goods by 20%. What is the profit percentage?

Discuss
Solution:
Let CP = Rs. 100, then SP will be 120.
He gives cloth worth Rs. 80 instead of Rs. 100.
Hence,
% Profit = 120−8080×100=50%
77. A traders sells two acrticles, one at a loss of 10% and another at a profit of 15% but finally there is no loss or gain. If the total sale price of these two articles is Rs. 30,000, find the difference between their cost prices:

Discuss
Solution:
10% of x = 15 % of y, where x + y = 30000
xy=3k2k
Hence, difference = k = Rs. 6000
78. The difference between a discount 40% on Rs. 500 and two successive discounts of 30% and 10% the same amount is:

Discuss
Solution:
40% discount on 500 = 40×500100   = Rs. 200
Two successive discount 30% and 10% on 500 would be
500 ===30% discount ⇒ Rs. 350
350 ===10% discount = 315
Total discount in first case = Rs. 200
Total discount in second case = 500 - 315 = Rs. 185
So, difference = Rs. 15
79. A person having bought goods for Rs. 400 sells half of it at a gain of 5%, at what gain % must he sell the remainder so as to gain 20% on the whole?

Discuss
Solution:
To gain 20% on whole he must sell all good for,
Rs. 400 + 20% of 400 = 480
As he get 5% gain on half of the goods i.e.
200 + 5% of 200 = 210
So required balance = 480 - 210 = 270
He must gain Rs. 70 on rest Rs. 200
% gain on remainder goods = 70×100200   = 35%
80. Find the difference of amount if 40% discount is given on Rs. 500 and two consecutive discount 30% and 10% are given on the same amount.

Discuss
Solution:
40% discount on 500 = 40×500100  = Rs. 200
Two successive discount on 500,
= 30% of 500 + 10% of (500 - 30% of 500)
= 150 + 10% of 350
= 150 + 35 = Rs. 185
Difference in Discount = 200 - 185 = Rs. 15

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