41. While selling a watch, a shop-keeper gives a discount of 5%. If he gives a discount of 7%, he earns Rs.15 less as profit. The marked price of the watch is :
a. Rs.697.50
b. Rs.712.50
c. Rs.787.50
d. None of these

Answer: D

Explanation:
Let the marked price be Rs. x
Then (7% of x ) - 15 = 5% of x
or $\displaystyle\frac{{7x}}{{100}} - \displaystyle\frac{{5x}}{{100}} = 15$ or x =750

42. A shop-keeper earns a profit of 12% on selling a book at 10% discount on the printed price. The ratio of the cost price and the printed price of the book is :
a. 45 : 56
b. 50 : 61
c. 99 : 125
d. None of these

Answer: A

Explanation:
Let the printed price of the book be Rs.100. After a discount of 10% S.P= Rs.90 Profit earned = 12%
C.P. of the book = Rs.$\left[ {\displaystyle\frac{{100}}{{112}} \times 90} \right]$=Rs.$\displaystyle\frac{{1125}}{{14}}$
Hence, (C.P) : (Printed price)= $\displaystyle\frac{{1125}}{{14}}$:100
or 45:56

43. A retailer buys a sewing machine at a discount of 15% and sells it for Rs.1955. Thus he makes a profit of 15%. The discount is :
a. Rs.270
b. Rs.290
c. Rs.300
d. None of these

Answer: C

Explanation:
Cost price for the retailer = $\displaystyle\frac{{100}}{{(100 + 15)}} \times 1955 = 1700$
But this price is what retailer got after having got a discount of 15%.
Let the marked price be Rs.x . Purchase price by the retailer = (100-15)% of Rs.x.
So $\displaystyle\frac{{85}}{{100}} \times x = 1700 \Rightarrow x = 2000$
Discount received by retailer = (15% of Rs.2000) = Rs.300

44. An umbrella marked at Rs.80 is sold for Rs.68. The rate of discount is :
a. 15%
b. 12%
c. $17\displaystyle\frac{{11}}{{17}}$%
d. 20%

45. Kabir buys an article with 50% discount on its marked price. He makes a profit of 10% by selling it at Rs.660. The marked price is :
a. Rs.600
b. Rs.700
c. Rs.800
d. 685

Answer: C

Explanation:
Cost price for Kabir = $\displaystyle\frac{{100}}{{100 + 10}} \times 660 = 600$
But this price is what he got after having a discount of 50%. Let the marked price be x.
Then (100 - 25)% of x = 600 $ \Rightarrow $ x = Rs.800

Alternatively:
Let the original price be Rs.x
C.P = (x - 50% of x ) = $\displaystyle\frac{{3x}}{4}$
S.P = $\left[ {\displaystyle\frac{{3x}}{4} + 10\% {\rm\text{ of }}\displaystyle\frac{{3x}}{4}} \right] = \displaystyle\frac{{33x}}{{40}}$
$\displaystyle\frac{{33x}}{{40}}$=660$ \Rightarrow $x=800

46. The ratio of the prices of three different types of cars is 4:5:7. If the difference between the costliest and the cheapest cars is Rs.60000, the price of the car of modest price is :
a. Rs.80000
b. Rs.100000
c. Rs.140000
d. Rs.120000

Answer: B

Explanation:
Let the price be 4x, 5x and 7x rupees.
Then, 7x - 4x = 60000
$ \Rightarrow $ x = 20000.
Required price = 5x = Rs.100000.

47. A discount series of 10%, 20% and 40% is equal to a single discount of :
a. 50%
b. 56.8%
c. 60%
d. 70.28%

Answer: B

Explanation:
Let original price = Rs.100. Price after first discount = Rs.90. Price after second discount
= Rs. $\left[ {\displaystyle\frac{{80}}{{100}} \times 90} \right]$=Rs.72
Price after third discount = Rs.$\left[ {\displaystyle\frac{{60}}{{100}} \times 72} \right]$ = Rs.43.20
Single discount = (100 - 43.20) = 56.8%

48. Subhash purchased a tape recorder at $\displaystyle\frac{9}{{10}}th$ of its selling price and sold it at 8% more than its S.P. His gain is :
a. 8%
b. 10%
c. 18%
d. 20%

Answer: D

Explanation:
Let the S.P be Rs.x
Then, C.P paid by Subhash = Rs.${\displaystyle\frac{{9x}}{{10}}}$
S.P. received by Subhash = (108% of Rs.x) = Rs.${\displaystyle\frac{{27x}}{{25}}}$
Gain = Rs.$\left[ {\displaystyle\frac{{27x}}{{25}} - \displaystyle\frac{{9x}}{{10}}} \right]$=Rs.$\displaystyle\frac{{9x}}{{50}}$
Hence Gain % =$\left[ {\displaystyle\frac{{9x}}{{50}} \times \displaystyle\frac{{10}}{{9x}} \times 100} \right]$% = 20%

Alternatively:
Assume Selling price is 100. So he gets it for 90 and sold it for 108. His profit is 18. Profit percentage is 18/90 x 100 = 20%
Easy. is it not!!