31. Which of the following successive discounts is better to a customer?
    (a) 20%, 15%, 10% or
    (b) 25%, 12%, 8% ?

1. 1. (a) is better

   
   
   

   2. (b) is better

   
   
   

   3. (a) or (b) (both are same)

   
   
   

   4. None of these

   
   
   

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1. View Hint View Answer Discuss in Forum

   (a) Single equivalent discount for 20% and 15%
   

   =		20 + 15 −	20 × 15		% = 32%
   			100

   
   (b) Single equivalent discount for 25% and 12%
   

   =		25 + 12 −	25 × 12		% = 34%
   			100

   
   Alternate method to solve this question :
   Case I.
   D₁ = 20%, D₂ = 15%, D₃ = 10%
   

   Equivalent discount = 100 −

   100 − D1

   100 − D2

   100 − D3

   × 100

   100

   100

   100

   
   
   Case II.
   D₁ = 25%, D₂ = 12%, D₃ = 8%
   

   Equivalent discount = 100 −

   100 − D1

   100 − D2

   100 − D3

   × 100

   100

   100

   100

   Correct Option: B

   (a) Single equivalent discount for 20% and 15%
   

   =		20 + 15 −	20 × 15		% = 32%
   			100

   
   Single equivalent discount for 32% and 10%
   

   =		32 + 10 −	32 × 10		% = 38.8%
   			100

   
   (b) Single equivalent discount for 25% and 12%
   

   =		25 + 12 −	25 × 12		% = 34%
   			100

   
   Single equivalent discount for 34% and 8%
   

   =		34 + 8 −	34 × 8		% = 42 – 2.72 = 39.28%
   			100

   
   Alternate method to solve this question :
   Case I.
   D₁ = 20%, D₂ = 15%, D₃ = 10%
   

   Equivalent discount = 100 −

   100 − D1

   100 − D2

   100 − D3

   × 100

   100

   100

   100

   
   

   Equivalent discount = 100 −

   100 − 20

   100 − 15

   100 − 10

   × 100

   100

   100

   100

   
   

   Equivalent discount = 100 −		80	×	85	×	90	× 100
   		100		100		100

   
   Equivalent discount = 100 – 61.2 = 38.8%
   Case II.
   D₁ = 25%, D₂ = 12%, D₃ = 8%
   

   Equivalent discount = 100 −

   100 − D1

   100 − D2

   100 − D3

   × 100

   100

   100

   100

   
   

   Equivalent discount = 100 −

   100 − 25

   100 − 12

   100 − 8

   × 100

   100

   100

   100

   
   

   Equivalent discount = 100 −		75	×	88	×	92	× 100
   		100		100		100

   
   Equivalent discount = 100 – 60.72 = 39.28%
   ⇒  Case II is better than Case I.

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32. An article is marked at ₹ 5,000. The shopkeeper allows successive discounts of x%, y%, z% on it. The net selling price is

1. 1. ₹	(100 − x)(100 + y)(100 + z)
      	200

   
   
   

   2. ₹	(100 + x)(100 + y)(100 − z)
      	200

   
   
   

   3. ₹	(100 − x)(100 − y)(100 − z)
      	200

   
   
   

   4. ₹	(100 − x)(100 + y)(100 − z)
      	200

   
   
   

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1. View Hint View Answer Discuss in Forum

   Required S.P = 5000 ×	(100 − x)	×	(100 − y)	×	(100 − z)
   	100		100		100

   Correct Option: C

   Required S.P = 5000 ×	(100 − x)	×	(100 − y)	×	(100 − z)
   	100		100		100

   
   

   Required S.P = ₹		(100 − x)(100 − y)(100 − z)
   		200

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33. The difference between a discount of 30% and two successive discounts of 20% and 10% on the marked price of an article is Rs. 144. The marked price of the article is

1. 1. Rs. 7,200

   
   
   

   2. Rs. 7,400

   
   
   

   3. Rs. 7,500

   
   
   

   4. Rs. 7,000

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the marked price of article be Rs. M.
   

   Single equivalent discount for X % and Y % =		x + y −	xy		%
   			100

   
   

   Single equivalent discount for 20% and 10% =		20 + 10 −	20 × 10		% = 28%
   			100

   
   According to the question,
   
   30% of M – 28% of M = 144
   Solve this equation further to calculate the Marked price of the article.

   Correct Option: A

   Let the marked price of article be Rs. M.
   

   Single equivalent discount for X % and Y % =		x + y −	xy		%
   			100

   
   

   Single equivalent discount for 20% and 10% =		20 + 10 −	20 × 10		% = 28%
   			100

   
   According to the question,
   
   30% of M – 28% of M = 144
   

   ⇒	M × 2	= 144
   	100

   
   

   ⇒  M =	144 × 100
   	2

   
   ⇒  M = Rs. 7200

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34. Allowing 20 % and 15 % successive discounts, the selling price of an article becomes Rs. 3,060; then the marked price will be

1. 1. Rs. 4,000

   
   
   

   2. Rs. 4,400

   
   
   

   3. Rs. 5,000

   
   
   

   4. Rs. 4,500

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let us assume the Marked price of article = Rs. M
   According to the question,
   

   M ×	80	×	85	= 3060
   	100		100

   
   Alternate method to solve this question :
   
   According to given question.
   Here, S.P. = Rs. 3060, M.P. = ?, D₁ = 20%, D₂ = 15%
   
   

   S.P = M.P		100 − D1			100 − D2
   		100			100

   3060 = M.P.		100 − 20			100 − 15
   		100			100

   
   
   

   Correct Option: D

   Let us assume the Marked price of article = Rs. M
   According to the question,
   

   M ×	80	×	85	= 3060
   	100		100

   
   

   ⇒  M =	3060 × 100 × 100
   	80 × 85

   
   M = Rs. 4500
   Alternate method to solve this question :
   According to given question.
   Here, S.P. = Rs. 3060, M.P. = ?, D₁ = 20%, D₂ = 15%
   
   

   S.P = M.P		100 − D1			100 − D2
   		100			100

   
   

   3060 = M.P.		100 − 20			100 − 15
   		100			100

   3060 = M.P.		80	×	85
   		100		100

   
   

   M.P. =	3060 × 10000
   	80 × 85

   
   M.P. = Rs. 4500

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35. In order that there may be a profit of 20% after allowing a discount of 10% on the marked price, the cost price of an article has to be increased by

1. 1. 30%

   
   
   

   2. 33%

   
   
   

   3. 33¹/₃%

   
   
   

   4. 33²/₃%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let MP = ₹ N
   ∴ SP = N x (100 - 10)/100 = ₹ 9N/10
   ∴ CP = (9N/10) x [100/(100 + 20)] = ₹ 3N/4
   Thus, CP has to be increased by = [(N - 3N/4) / (3N/4)] x 100%

   Correct Option: C

   Let MP = ₹ N
   ∴ SP = N x (100 - 10)/100 = ₹ 9N/10
   ∴ CP = (9N/10) x [100/(100 + 20)] = ₹ 3N/4
   Thus, CP has to be increased by = [(N - 3N/4) / (3N/4)] x 100%
   = [(N/4) / (3N/4)] x 100 %
   = 33¹/₃ %

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