33. A dealer marks his goods 20% above cost price. He then allows some discount on it and makes a profit of 8%. The rate of discount is :
a. 12%
b. 10%
c. 6%
d. 4%

34. A cloth merchant has announced 25% rebate in prices. If one needs to have a rebate of Rs.40, then how many shirts, cash costing Rs.32, he should purchase ?
a. 6
b. 5
c. 10
d. 7

Answer: B

Explanation:
Suppose the number of shirts = x.
Then, rebate = $\left[ {\displaystyle\frac{{25}}{{100}} \times 32x} \right] = 8x$
8x = 40 or x = 5.

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35. The price of an article was increased by p%. Later the new price was decreased by p%. If the latest price was Rs.1, the original price was :
a. Rs. 1
b. $\left[ {\displaystyle\frac{{1 - {p^2}}}{{100}}} \right]$
c. $\left[ {\displaystyle\frac{{10000}}{{10000 - {p^2}}}} \right]$
d. $\left[ {\sqrt {\displaystyle\frac{{1 - {p^2}}}{{100}}} } \right]$

Answer: C

Explanation:
Let the original price = Rs.x
Price after P% increase = (100+P)% of x
= $\displaystyle\frac{{(100 + P)x}}{{100}}$
New price after P% decrease
= (100-P)% of $\left[ {\displaystyle\frac{{(100 + P)x}}{{100}}} \right]$
= $\displaystyle\frac{{(100 - P)}}{{100}} \times \displaystyle\frac{{(100 + P)}}{{100}} \times x$
= $\displaystyle\frac{{(100 - P)(100 + P)}}{{100 \times 100}} \times x = 1$
or x = $\displaystyle\frac{{100 \times 100}}{{(100 - P)(100 + P)}} = \displaystyle\frac{{10000}}{{10000 - {P^2}}}$

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36. The difference between the selling prices after a discount of 40% on Rs.500 and two successive discount of 36% and 4% on the same amount is :
a. 0
b. Rs.2
c. Rs.1.93
d. Rs.7.20

Answer: D

Explanation:
Sale after 40% discount = 60% of Rs.500 = Rs.300.
Price after 36% discount = 64% of Rs.500 = Rs.320.
Price afdter next 4% discount = 96% of Rs.320 = Rs.307.20
Difference in two prices = Rs.7.20

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37. Tarun bought a T.V with 20% discount on the labelled price. Had he bought it with 25% discount, he would have saved Rs.500. At what price did he buy the T.V ?
a. Rs.5000
b. Rs.10,000
c. Rs.12000
d. Rs.6000

Answer: B

Explanation:
Let the labelled price be Rs.100, S.P in 1st case = Rs.80, S.P in 2nd case = Rs.75. If saving is Rs.5, labelled price
= Rs.$\left[ {\displaystyle\frac{{(100}}{5} \times 500} \right]$
= Rs.10000

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38. A man purchases an electric heater whose printed price is Rs.160. If he received two successive discounts of 20% and 10%; he paid :
a. Rs.112
b. Rs.129.60
c. Rs.119.60
d. Rs.115.20

Answer: D

Explanation:
Price after Ist discount = 100% of Rs.160 = Rs. 128
Price after 2nd discount = 90% of Rs.128 = Rs.115.20

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39. The marked price is 10% higher than the cost price. A discount of 10% is given on the marked price. In this kind of sale, the seller
a. bears no loss, no gain
b. gains
c. losses
d. None of these

Answer: C

Explanation:
Let C.P = Rs.100
Marked price = Rs.110
S.P = 90 % of Rs.110 = Rs.99
Loss = 1%

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40. A trader lists his articles 20% above C.P and allows a discount of 10% on cash payment. His gain percent is :
a. 10%
b. 8%
c. 6%
d. 5%

Answer: B

Explanation:
Let C.P = Rs.100
Then, marked price = Rs.120
S.P = 90% of Rs.120= Rs.108
Gain = 8%