17. A merchant professes to sell goods at 20% profit but uses weight of 900 grams in place of a kilogram. What is his actual profit per cent?
a. 28%
b. 30%
c. 33.33%
d. 35%

Answer: C

Explanation:
Assume 1gm costs 1 rupee. The merchant gives 900 grams charging the price of 1200 grams.
Therefore, His gain is 300 grams on every 900 grams or on investment of Rs.900 his gain is Rs.300.
Therefore, Profit per cent = $\displaystyle\frac{{{\rm{300}}}}{{{\rm{900}}}}$ x 100 = 33.33%

18. A shopkeeper buys some pens. If he sells them at Rs.13 per pen, his total loss in Rs.150 but on selling them at Rs.15 per pen, his total gain is Rs. 100. How many pens did he sell?
a. 101
b. 111
c. 121
d. 125

Answer: D

Explanation:
Difference in sales amount due to change in selling price = Rs. 150 + Rs. 100 = Rs. 250
Difference in selling price per pen = Rs. 15 - Rs. 13 = Rs. 2
Therefore, On selling 1 pen, sales amount is increased by Rs. 2 in second case.
Therefore, Total pens sold = $\displaystyle\frac{{{\rm{250}}}}{{\rm{2}}}$ = 125 pens

19. A man sold an article at 10% profit. Had it been sold for Rs. 50 more, he would have gained 15%. Cost Price of the article is:
a. 9500
b. 9600
c. 9800
d. 1000

Answer: D

Explanation:
Let us assume cost price of the article is Rs.100x. then selling price = 110x. But if he sold the product for Rs.50 more his profit is 15%. In this case his selling price is 115x. But the difference in the selling prices were gives as Rs.50. So 115x - 110x = 50, therefore x = 10. Substituting in cost price, CP = Rs.1000

Alternate method:
Difference in two selling prices = 15% - 10% = 5% of cost price
Actual difference in two selling price = Rs. 50 (i.e. 10 times of 5)
Therefore, Cost Price = 10 × Rs. 100 = Rs. 1000

20. A machine is sold at a loss of 10%. Had it been sold at a profit of 15%, it would have fetched Rs. 50 more. The cost price of the machine is:
a. Rs.210
b. Rs.220
c. Rs.200
d. Rs.270

Answer: C

Explanation:
Let us assume cost price of the article is Rs.100x. then selling price = 90x. But if he sold the product for Rs.50 more his profit is 15%. In this case his selling price is 115x. But the difference in the selling prices were gives as Rs.50. So 115x - 90x = 50, therefore x = 2. Substituting in cost price, CP = Rs.200

Alternate method:
Difference in two selling prices = 10% - (-15%) = 10% + 15% = 25% of cost price
Actual difference in two selling price = Rs. 50 (i.e. 2 times of 25)
25%(CP) = 50
CP = 4 × 50 = Rs. 200

21. A bicycle is sold at 10% profit. Had it been sold for Rs. 10 less, the profit would have been 5% only. What is the cost price of the bicycle?
a. 180
b. 200
c. 220
d. 250

Answer: B

Explanation:
Let us assume cost price of the article is Rs.100x.
Then selling price = 110x.
But if he sold the bicycle for Rs.10 less his profit is 5%. In this case his selling price is 105x.
But the difference in the selling prices were gives as Rs.10.
So 110x - 105x = 10, therefore x = 2.
Substituting in cost price, CP = Rs.200

Alternative Method:
Difference in two selling prices = 10% - 5% = 5% of cost price
Actual difference in two selling price = Rs. 10
5%(CP) = 10
CP = 20 × 10 = Rs. 200

22. A man sells an article at a profit of 25%. If he had bought it at 20% less and sold it for Rs. 10.50 less, he would have gained 30%. Find the CP of the article.
a. 144
b. 72
c. 36
d. None of these

Answer: C

Explanation:
Let the cost price = x ; Selling Price = 125%(x)
New Cost Price = 80%(x) ;
New SP = 125%(x) – 10.50
But new SP = 130% of new CP =130%(80%x)
Therefore, 130%(80%x) = 125%(x) – 10.50
$ \Rightarrow 104\% (x) = 125\% (x) - 10.50$
$ \Rightarrow 21\% (x) = 10.50$ $ \Rightarrow x = 10.50 \times \displaystyle\frac{{100}}{{21}} \Rightarrow Rs.50$

Alternate Method:
Let the CP be Rs. 100x. So, SP is Rs. 125x.
The new CP is Rs. 80x. So the new SP =130%(80x)= Rs. 104x
So the difference of SP’s = Rs. 21x.
21x = 10.5
x = 1/2
CP = $\dfrac{1}{2} \times 100$ = Rs.50

23. A shopkeeper purchases goods at $\displaystyle\frac{{{\rm{19}}}}{{{\rm{20}}}}$ of its marked price and sells them at 14% more than its marked price. Find his profit per cent.
a. 12.50%
b. 15%
c. 20%
d. 37.5%

Answer: C

Explanation:
Let marked price of the goods = Rs. 100. Then cost price = Rs. 100 x $\displaystyle\frac{{{\rm{19}}}}{{{\rm{20}}}}$ = Rs. 95
Selling price = Rs. 100 + 14% of Rs. 100 = Rs. 114
Therefore, Profit = Rs. 114 - 95 = Rs. 19 on Rs. 95
Therefore, Profit = $\dfrac{{{\rm{19}}}}{{{\rm{95}}}}{\rm{ = }}\dfrac{{\rm{1}}}{{\rm{5}}}$ = 20%

24. A merchant fixed selling price of his articles at Rs.700 after adding 40% profit to the cost price. As the sale was very low at this price level, he decided to fix the selling price at 10% profit. Find the new selling price.
a. 600
b. 800
c. 925
d. 1200