251. Alex sold his goods after announcing two successive discounts of 30% each. The effective discount altogether is

1. 1. 52%

   
   
   

   2. 49%

   
   
   

   3. 50%

   
   
   

   4. 51%

   
   
   

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1. View Hint View Answer Discuss in Forum

   As we know the formula for two successive discount.
   

   Equivalent single discount =		D1 + D2 −	D1 × D2		%
   			100

   
   

   Correct Option: D

   As we know the formula for two successive discount.
   

   Equivalent single discount =		D1 + D2 −	D1 × D2		%
   			100

   
   

   Single equivalent discount =		30 + 30 −	30 × 30		% = 51%
   			100

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252. A sofa-set listed at ₹ 800 is sold to a retailer at successive discounts of 25% and 15% by the wholesaler. Then the cost price of the sofa-set for retailer is

1. 1. ₹ 500

   
   
   

   2. ₹ 510

   
   
   

   3. ₹ 550

   
   
   

   4. ₹ 560

   
   
   

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1. View Hint View Answer Discuss in Forum

   Use the below formula to calculate the Equivalent single discount.
   

   Equivalent single discount =		D1 + D2 −	D1 × D2		%
   			100

   
   

   Single equivalent discount =		25 + 15 −	25 × 15
   			100

   
   Single equivalent discount = 40 – 3.75 = 36.25
   

   Correct Option: B

   Use the below formula to calculate the Equivalent single discount.
   

   Equivalent single discount =		D1 + D2 −	D1 × D2		%
   			100

   
   

   Single equivalent discount =		25 + 15 −	25 × 15
   			100

   
   Single equivalent discount = 40 – 3.75 = 36.25
   

   ∴  C.P. for the retailer =	800 × (100 − 36.25)	= ₹ 510
   	100

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253. A single discount of 50% on an article costing ₹ 10000 is better than two successive discounts of 40% and 10% by

1. 1. ₹ 400

   
   
   

   2. ₹ 1000

   
   
   

   3. ₹ 500

   
   
   

   4. ₹ 600

   
   
   

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1. View Hint View Answer Discuss in Forum

   Single equivalent discount for 40% and 10%
   

   =		40 + 10 −	40 × 10		% = 46%
   			100

   
   Difference of percentage = 4%

   Correct Option: A

   Single equivalent discount for 40% and 10%
   

   =		40 + 10 −	40 × 10		% = 46%
   			100

   
   Difference of percentage = 4%
   ∴  Savings = 4% of 10000
   

   =	10000 × 4	= ₹ 400
   	100

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254. Two successive discounts of 70% and 30% are equivalent to a single discount of

1. 1. 75%

   
   
   

   2. 79%

   
   
   

   3. 100%

   
   
   

   4. 89%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Single equivalent discount =		70 + 30 −	70 × 30		%
   			100

   Correct Option: B

   Single equivalent discount =		70 + 30 −	70 × 30		%
   			100

   
   Single equivalent discount = (100 – 21)% = 79%
   2nd Method
   After a discount of 70%, remaining price is just 30. On this 30%, another discount of 30% is given which will be equal to 9 so, total discount = 70% + 9% =79%.

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255. A shopkeeper marks the price of an article at ₹ 80. What will be the selling price, if he allows two successive discounts of 5% each?

1. 1. ₹ 72.2

   
   
   

   2. ₹ 72

   
   
   

   3. ₹ 85

   
   
   

   4. ₹ 7.2

   
   
   

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1. View Hint View Answer Discuss in Forum

   Single equivalent discount =		5 + 5 −	25		%
   			100

   
   Alternate method to solve this question :
   Here, M.P. = 80, D₁ = 5%, D₂ = 5%, S.P. = ?
   

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

   
   

   S.P. = 80		100 − 5			100 − 5
   		100			100

   Correct Option: A

   Single equivalent discount =		5 + 5 −	25		%
   			100

   
   

   Single equivalent discount = 9	3	=	39	%
   	4		4

   
   

   ∴  S.P. = 80 ×	361	= ₹ 72.2
   	400

   
   Alternate method to solve this question :
   Here, M.P. = 80, D₁ = 5%, D₂ = 5%, S.P. = ?
   

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

   
   

   S.P. = 80		100 − 5			100 − 5
   		100			100

   
   

   S.P = 80 ×	95	×	95	= ₹ 72.2
   	100		100

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