25. A shopkeeper bought some apples at the rate of Rs. 16 per dozen. Due to harsh climate 20% of the apples bought were rotten during the transportation. At what rate of per dozen should he sell the remaining apples so as to gain 30% on the total cost price?
a. 20
b. 26
c. 28
d. 30

Answer: B

Explanation:
Since, 20% of the quantity is spoiled, selling the apples at cost price will result in 20% loss.
Therefore, We are to find the selling price which gives him 30% profit instead of a loss of 20%.
Therefore, Selling Price = Rs. 16 × $\displaystyle\frac{{{\rm{130}}}}{{{\rm{80}}}}$ = Rs. 26 per dozen.

26. A Watch is sold at 10% discount on its marked price of Rs. 480. If the retailer makes 20% profit on the cost price, find the cost price of the watch.
a. Rs.300
b. Rs.360
c. Rs.400
d. Rs.420

27. A shopkeeper allows 25% discount on the marked price of his articles and hence gains 25% of the Cost Price. What is the marked price of the article on selling which he gains Rs. 120?
a. Rs.75
b. Rs.76
c. Rs.70
d. Rs.80

Answer: A

Explanation:
Marked price of the article = Rs. 120 × $\dfrac{{125}}{{25}} \times \dfrac{{100}}{{75}}$ = Rs. 800
Hint: If profit is Rs. 25, then Selling price = Rs. 100 + Rs. 25 = Rs. 125.
If marked price is Rs. 100, then Selling price = Rs. 100 - Rs. 25 = Rs. 75.

28. A man purchased two articles for Rs. 10000 each. On selling first, he gains 20% and on the other, he loses 20%. What is profit/loss in the transaction?
a. 4% Profit
b. 4% Loss
c. 40% Profit
d. No Profit and No loss

Answer: D

Explanation:
Here, the cost price of both the articles are same.
Profit made on one item is exactly equal to loss suffered on the other.
Therefore, No profit, no loss.

29. A man sold two articles for Rs. 10000 each. On selling first, he gains 10% and on the other, he loses 10%. What is profit/loss in the transaction.
a. 20% Profit
b. 1% Profit
c. 1% Loss
d. 4% Loss

Answer: C

Explanation:
Loss % = $\displaystyle\frac{{\left( {{\rm\text{Common Gain and Loss}}} \right)^{\rm{2}} }}{{{\rm{100}}}}{\rm{ = }}\displaystyle\frac{{{\rm{10}}^{\rm{2}} }}{{{\rm{100}}}}$ = 1%

30. Two tables are purchased for the total cost of Rs. 5000. First table is sold at 40% profit and second at 40% loss. If selling price is same for both the tables, what is the cost price of the table that was sold at profit?
a. Rs.1260
b. Rs.1500
c. Rs.2500
d. Rs.2600

Answer: B

Explanation:
140% of cost price of first table = 60% of cost price of second table.
Cost price of first table : Cost price of second table = 60 : 140 = 3 : 7
Therefore, Cost price of first table = $\displaystyle\frac{{\rm{3}}}{{{\rm{10}}}}$ × 5000 = Rs. 1500.

31. A reduction of 10% in the price of sugar enables a man to buy 25 kg more for Rs. 225. What is the original price of sugar (per kilogram)?
a. Rs.3500
b. Rs.4000
c. Rs.4500
d. Rs.5000

Answer: B

Explanation:
Let the original price be x. Then Original quantity = $\displaystyle\frac{{{\rm{225}}}}{{\rm{x}}}$
New price = 90%(x) (if a number reduced by 10% it becomes 90% of the original number)
New quantity = $\;\displaystyle\frac{{225}}{{0.9{\kern 1pt} x}}$
Equating $\displaystyle\frac{{225}}{{0.9{\kern 1pt} x}}\; - \;\frac{{225}}{x}\; = 25$
$ \Rightarrow x = Rs.1$

Alternate method:

If we keep quantity constant, and price got changed by K%, expenditure also got changed by K%
When the price of the sugar got reduced by 10%, Now we could pay 10% less than the actual expenditure. But used the savings to take extra 25 kgs of sugar so
CP of 25 kg = $\displaystyle\frac{{10}}{{100}}\,{\kern 1pt} \times \,\,225\,\, = \,\,Rs.\,\,22.5\,;$
Reduced CP of 1 kg = $\displaystyle\frac{{22.5}}{{25}}\, = \,{\mathop{\rm Re}\nolimits} .\,\,0.90$
We got this reduced price after we reduced the original cost price by 10%. To calculate the original cost price we need to divide =Original price of sugar (per kg) can b = $\dfrac{{0.90}}{{90}}{\mkern 1mu} {\kern 1pt} \times {\mkern 1mu} {\kern 1pt} 100{\mkern 1mu} {\kern 1pt} {\mkern 1mu} {\kern 1pt} = {\mkern 1mu} {\kern 1pt} {\mkern 1mu} {\kern 1pt} {\text{Rs}}.{\mkern 1mu} {\kern 1pt} 1{\mkern 1mu} {\kern 1pt} .$
Since the price is reduced by 10% (i.e.$\displaystyle\frac{1}{{10}}$) the new price has become $\displaystyle\frac{9}{{10}}$ the original. So, the consumption becomes the $\displaystyle\frac{{10}}{9}$, i.e. an increase of $\displaystyle\frac{1}{9}$
Therefore by unitary method,

32. The income of a broker remains unchanged though the rate of commission is increased from 4% to 5%. The percentage of slump in business is :
a. 8%
b. 1%
c. 20%
d. 80%

Answer: C

Explanation:
Let the business value changes from x to y.
Then, 4% of x = 5% of y or $\displaystyle\frac{4}{{100}} \times x = \displaystyle\frac{5}{{100}}\times y$
or y = $\displaystyle\frac{4}{5}x$
Change in business = $\left( {x - \displaystyle\frac{4}{5}x} \right) = \displaystyle\frac{1}{5}x$
Percentage slump in business
= $\left( {\displaystyle\frac{1}{5}x \times \displaystyle\frac{1}{x} \times 100} \right)$%