6. A company offers three types of successive discounts : (i) 25% and 15%, (ii) 30% and 10%, (iii) 35% and 5%. Which offer is the best for a customer?

1. 1. First offer

   
   
   

   2. Second offer

   
   
   

   3. Third offer

   
   
   

   4. Any one; all are equally good

   
   
   

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1. View Hint View Answer Discuss in Forum

   We know that ,
   Successive discounts :-
   

   a + b -	ab	%
   	100

   Correct Option: C

   (i) Here , a = 25% and b = 15%,
   

   Equivalent discount = 25 + 15 -	25 x 15	%
   	100

   
   Equivalent discount = ( 40 - 3.75 ) % = 36.25%
   (ii) Here , a = 30% and b = 10%,
   

   Equivalent discount = 30 + 10 -	30 x 10	%
   	100

   
   Equivalent discount = ( 40 - 3 ) % = 37%
   (iii) Here , a = 35% and b = 5%,
   

   Equivalent discount = 35 + 5 -	35 x 5	%
   	100

   
   Equivalent discount = ( 40 - 1.75 ) % = 38.25%
   From above , it is clear that discount 38.25% is best for a customer.
   Hence option [ C ] is correct answer.

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7. The difference between a discount of 40% on $ 500 and two successive discounts of 36%, 4% on the same amount is :

1. 1. $ 0

   
   
   

   2. $ 2

   
   
   

   3. $ 1.93

   
   
   

   4. $ 7.20

   
   
   

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1. View Hint View Answer Discuss in Forum

   Single equivalent discount for 36% and 4% i.e.
   Here , a = 36% and b = 4%
   

   Equivalent discount = a + b -	a x b	%
   	100

   
   

   Equivalent discount = 36 + 4 -	36 x 4	%
   	100

   
   

   Correct Option: D

   Single equivalent discount for 36% and 4% i.e.
   Here , a = 36% and b = 4%
   

   Equivalent discount = 36 + 4 -	36 x 4	%
   	100

   
   Equivalent discount = ( 40 - 1.44 )% = 38.56%
   Therefore, required difference = 1.44% of 500
   

   =	1.44	x 500 = $ 7.20
   	100

   
   

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8. Successive discounts of 10 %, 20 % and 30 % is equivalent to a single discount of :

1. 1. 60 %

   
   
   

   2. 49.6 %

   
   
   

   3. 40.5 %

   
   
   

   4. 36 %

   
   
   

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1. View Hint View Answer Discuss in Forum

   Single equivalent discount for successive discounts of 10% and 20%
   Here , a = 10% and b = 20%
   

   Equivalent discount = a + b -	a x b	%
   	100

   
   

   =		10 + 20 -	20 x 10		%
   			100

   
   = 28 %

   Correct Option: B

   Single equivalent discount for successive discounts of 10% and 20%
   Here , a = 10% and b = 20%
   

   Equivalent discount = a + b -	a x b	%
   	100

   
   

   =		10 + 20 -	20 x 10		%
   			100

   
   = 28 %
   Single equivalent discount for 28% and 30%
   Here , a = 28% and b = 30%
   

   Equivalent discount = a + b -	a x b	%
   	100

   
   

   =		28 + 30 -	28 x 30		%
   			100

   
   = 49.6 %
   

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9. A man buys a single apple for $ 25. If he were to buy a dozen apples, he would have to pay a total amount of $ 250. What would be the approximate % discount he would get on buying a dozen apples?

1. 1. 32

   
   
   

   2. 20

   
   
   

   3. 12

   
   
   

   4. 17

   
   
   

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1. View Hint View Answer Discuss in Forum

   Given :- Cost of one apple = $ 25
   ∴ Cost of 12 apples ( M.P. ) = 25 × 12 = $ 300
   Amount paid = $ 250
   Discount = 300 - 250 = $ 50
   

   Discount% =	Discount	x 100%
   	Marked Price

   Correct Option: D

   Given :- Cost of one apple = $ 25
   ∴ Cost of 12 apples ( M.P. ) = 25 × 12 = $ 300
   Amount paid = $ 250
   Discount = 300 - 250 = $ 50
   

   Discount% =	Discount	x 100%
   	Marked Price

   
   

   % Discount =	50 x 100	= 17 % (approx.)
   	300

   
   

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10. If on a marked price, the difference of selling prices with a discount of 30 % and two successive discounts of 20 % and 10 % is $ 72, then the marked price (in rupees) is :

1. 1. 3,600

   
   
   

   2. 3,000

   
   
   

   3. 2,500

   
   
   

   4. 2,400

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let the marked price be $ x
   Therefore, in case 1,
   

   Selling Price ( SP1 ) = $	70x	%
   	100

   
   Single discount equivalent to successive discounts of 20% and 10%.
   Here , a = 20% and b = 10%
   

   Equivalent discount = a + b -	a x b	%
   	100

   
   

   Equivalent discount = 20 + 10 -	20 x 10	%
   	100

   
   = ( 30 - 2 ) % = 28%
   

   In case 2 ,Selling Price ( SP2 ) = $	72x
   	100

   Correct Option: A

   Let the marked price be $ x
   Therefore, in case 1,
   

   Selling Price ( SP1 ) = $	70x	%
   	100

   
   Single discount equivalent to successive discounts of 20% and 10%.
   Here , a = 20% and b = 10%
   

   Equivalent discount = a + b -	a x b	%
   	100

   
   

   Equivalent discount = 20 + 10 -	20 x 10	%
   	100

   
   = ( 30 - 2 ) % = 28%
   

   In the case 2 , Selling Price ( SP2 ) = $	72x
   	100

   
   Therefore, SP₂ - SP₁
   

   $	72x	-	70x	= $ 72
   	100		100

   
   

   ⇒	2x	= 72
   	100

   
   ⇒ 2x = 7200
   

   ⇒ x =	7200
   	2

   
   x = $ 3600
   Hence , the marked price is $ 3600 .

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