49. At what price must Kantilal sell a mixture of 80kg. Sugar at Rs.6.75 per kg. with 120 kg. at Rs.8 per kg. to gain 20% ?
a. Rs.7.50 per kg
b. Rs.8.20 per kg
c. Rs.8.85 per kg
d. Rs.9 per kg.

Answer: D

Explanation:
Total C.P of 200 kg of sugar = Rs.$(80 \times 6.75 + 120 \times 8)$ = Rs.1500
C.P of 1 kg = Rs.$\left[ {\displaystyle\frac{{1500}}{{200}}} \right]$ = Rs.7.50
Gain required = 20%
S.P of 1 kg = (120% of Rs.7.50) = Rs.$\left[ {\displaystyle\frac{{120}}{{100}} \times 7.50} \right]$ = Rs.9 per kg.

50. A person bought an article and sold it at a loss of 10%. If he had bought it for 20% less and sold it for Rs.55 more, he would have had a profit of 40%. The C.P.of the article is :
a. Rs.200
b. Rs.225
c. Rs.250
d. None of these

Answer: C

Explanation:
Let C.P = Rs.x. Then S.P = Rs.$\left[ {\displaystyle\frac{{90}}{{100}} \times x} \right]$ = Rs.$\left[ {\displaystyle\frac{9}{{10}}x} \right]$
New C.P = Rs.$\left[ {\displaystyle\frac{{80}}{{100}} \times x} \right]$=Rs.$\left[ {\displaystyle\frac{{4x}}{5}} \right]$
Now gain = 40%
New S.P = $\left[ {\displaystyle\frac{{140}}{{100}} \times \displaystyle\frac{{4x}}{5}} \right]$=Rs.$\left[ {\displaystyle\frac{{28}}{{25}}x} \right]$
${\displaystyle\frac{{28}}{{25}}x - \displaystyle\frac{9}{{10}}x = 55}$ or x = 250
Hence, C.P = Rs.250

Alternatively:
Assume Cost price is 100x. Then initial selling price is 90x (Why? 10% loss!)
Had he bought it for 20% less, then his cost price be 80x
Now on this 80x, he got a profit percentage of 40%. So new selling price is 140% (80x) = 112x
But the difference in selling prices is 55. So 112x - 90x = 22x = 55 $ \Rightarrow $ x = 5/2
Substituting this value in 100x we get cost price = Rs.250

51. The cost price of an article, which on being sold at a gain of 12% yields Rs.6 more than when it is sold at a loss of 12% is :
a. Rs.30
b. Rs.25
c. Rs.24
d. Rs.20

Answer: B

Explanation:
Let C.P = Rs.x. Then ${\displaystyle\frac{{112}}{{100}}x - \displaystyle\frac{{88}}{{100}}x = 6}$
or 24x = 600
or x =${\displaystyle\frac{{600}}{{24}} = 25}$
C.P = Rs.25

52. A man sells a car to his friend at 10% loss. If the friend sells it for Rs.54000 and gains 20%, the original C.P.of the car was :
a. Rs.25000
b. Rs.37500
c. Rs.50000
d. Rs.60000

Answer: C

Explanation:
S.P = Rs.54,000. Gain earned = 20%
C.P = Rs.$\left[ {\displaystyle\frac{{100}}{{120}} \times 54000} \right]$ = Rs. 45000
This is the price the first person sold to the second at at loss of 10%.
Now S.P = Rs.45000 and loss = 10%
C.P. Rs.$\left[ {\displaystyle\frac{{100}}{{90}} \times 45000} \right]$ = Rs.50000.

53. Bhajan Singh purchased 120 reams of paper at Rs.80 per ream. He spent Rs.280 on transportation, paid octroi at the rate of 40 paise per ream and paid Rs.72 to the coolie. If he wants to have a gain of 8% , what must be the selling price per ream ?
a. Rs.86
b. Rs.87.48
c. Rs.89
d. Rs.90

54. Of two mixers and one T.V cost Rs.7000, while two T.Vs and one mixer cost Rs.9800, the value of one T.V is :
a. Rs.2800
b. Rs.2100
c. Rs.4200
d. Rs.8400

Answer: C

Explanation:
2x + y = 7000 - - - (i)
x + 2y = 9800 - - - (ii)
Solving (i) and (ii), we get y = 4200

55. Profit after selling a commodity for Rs.425 is same as loss after selling it for Rs.355. The cost of the commodity is :
a. Rs.385
b. Rs.390
c. Rs.395
d. Rs.400

Answer: B

Explanation:
Let C.P = Rs.x. Then.
425 - x= x - 355 or 2x = 780 or x = 390.

56. A merchant sold his goods for Rs.75 at a profit percent equal to C.P. The C.P was :
a. Rs.40
b. Rs.50
c. Rs.60
d. Rs.70

Answer: B

Explanation:
Let C.P=Rs.x
x + x% of x = 75 or x + ${\displaystyle\frac{{{x^2}}}{{100}}}$ = 75 or
${{x^2} + 100x - 7500 = 0}$ or (x + 150)(x - 50) = 0
x = 50 (Neglecting x = - 150)