196. A single discount equivalent to discount series 20%, 20% and 10% is

1. 1. 50%

   
   
   

   2. 48.4%

   
   
   

   3. 42.4%

   
   
   

   4. 40.4%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Single equivalent discount for 20% and 20%
   

   =		20 + 20 −	20 × 20		% = 36%
   			100

   
   Single equivalent discount for 36% and 10%
   

   =		36 + 10 −	36 × 10		% = 42.4%
   			100

   Correct Option: C

   Single equivalent discount for 20% and 20%
   

   =		20 + 20 −	20 × 20		% = 36%
   			100

   
   Single equivalent discount for 36% and 10%
   

   =		36 + 10 −	36 × 10		% = 42.4%
   			100

   
   Alternate method to solve this question :
   

   = 100 −

   100 − D1

   100 − D2

   100 − D3

   × 100

   100

   100

   100

   
   

   = 100 −

   100 − 20

   100 − 20

   100 − 10

   × 100

   100

   100

   100

   
   

   = 100 −	80	×	80	×	90	× 100
   	100		100		100

   
   = 100 – 57.60 = 42.40

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197. The single discount which is equivalent to successive discounts of 20%, 15% and 10% is

1. 1. 32·7%

   
   
   

   2. 34·2%

   
   
   

   3. 36·9%

   
   
   

   4. 38·8%

   
   
   

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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 for 20 % and 15 %
   

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

   
   Single equivalent discount for 32% and 10%
   

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

   Correct Option: D

   Use the below formula to calculate the Equivalent single discount.
   

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

   
   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

   
   Alternate method to solve this question :
   Here, D₁ = 20%, D₂ = 15%,D₃ = 10%
   Single equivalent discount
   

   = 100 −

   100 − D1

   100 − D2

   100 − D3

   × 100

   100

   100

   100

   
   

   = 100 −

   100 − 20

   100 − 15

   100 − 10

   × 100

   100

   100

   100

   
   

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

   
   Hence Equivalent single discount = 100 – 61.20 = 38.80%

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198. An article marked at Rs. 540 is sold at Rs. 496.80 in an offseason offer. Then the rate of discount offered (in per cent) is

1. 1. 7

   
   
   

   2. 7.5

   
   
   

   3. 8

   
   
   

   4. 10

   
   
   

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1. View Hint View Answer Discuss in Forum

   Discount given
   = Rs. (540 – 496.80)
   = Rs. 43.20
   If the rate of discount be x%, then
   x% of 540 = 43.20
   

   ⇒	540 × x	= 43.20
   	100

   
   

   ⇒  x =	43.20 × 100	= 8%
   	540

   Correct Option: C

   Discount given
   = Rs. (540 – 496.80)
   = Rs. 43.20
   If the rate of discount be x%, then
   x% of 540 = 43.20
   

   ⇒	540 × x	= 43.20
   	100

   
   

   ⇒  x =	43.20 × 100	= 8%
   	540

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199. A dealer buys an article listed at Rs. 100 and gets successive discounts of 10% and 20%. He spends 10% of the cost price on transportation. At what price should he sell the article to earn a profit of 15%?

1. 1. ₹ 90.80

   
   
   

   2. ₹ 92.00

   
   
   

   3. ₹ 91.08

   
   
   

   4. ₹ 91.20

   
   
   

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1. View Hint View Answer Discuss in Forum

   Single equivalent discount =		10 + 20 −	10 × 20		%
   			100

   
   = (30 – 2)% = 28%
   ∴  C.P. of article = 100 – 28 = Rs. 72
   

   Actual cost price of article =	72 × 110	= Rs. 79.2
   	100

   
   ∴  For a profit of 15%,
   

   Required S.P. =	79.2 × 115	= Rs. 91.08
   	100

   Correct Option: C

   Single equivalent discount =		10 + 20 −	10 × 20		%
   			100

   
   = (30 – 2)% = 28%
   ∴  C.P. of article = 100 – 28 = Rs. 72
   

   Actual cost price of article =	72 × 110	= Rs. 79.2
   	100

   
   ∴  For a profit of 15%,
   

   Required S.P. =	79.2 × 115	= Rs. 91.08
   	100

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200. A company showroom gives a discount of 20% on the second grade shoes and a further
     discount of 15% on shareholder’s coupon. The total discount, a coupon holder will get is

1. 1. 32%

   
   
   

   2. 36%

   
   
   

   3. 35%

   
   
   

   4. 38%

   
   
   

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1. View Hint View Answer Discuss in Forum

   Required single discount =		x + y −	xy		%
   			100

   
   

   Required single discount =		20 + 15 −	20 × 15		%
   			100

   
   = (35 – 3)% = 32%

   Correct Option: A

   Required single discount =		x + y −	xy		%
   			100

   
   

   Required single discount =		20 + 15 −	20 × 15		%
   			100

   
   = (35 – 3)% = 32%

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