Discount
 If $ 10 be allowed as true discount on a bill of $ 110 due at the end of certain time, then the discount allowed on the same amount due at the end of double the time is :

 $ 20
 $ 21.81
 $ 22
 $ 18.33

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Given : Amount = $ 110
S.I. on $ (110  10) for a given time = $ 10
S.I. on $ 100 for double the time = $ 20
Sum = $ (100 + 20) = $ 120∴ True discount = Amount x Rate x Time 100 + Rate x Time Correct Option: D
Given : Amount = $ 110
S.I. on $ (110  10) for a given time = $ 10
S.I. on $ 100 for double the time = $ 20
Sum = $ (100 + 20) = $ 120∴ True discount = Amount x Rate x Time 100 + Rate x Time T.D. on $ 110 = $ 20 x 110 = $ 18.33 120
 A trader marks his goods at 20% above the cost price. If he allows a discount of 5% for cash down payment, his profit percent for such a transaction is

 15%
 12%
 14%
 17%

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Let C.P. be ₹ 100.
Marked price = ₹ 120S.P. = 120 × 95 = ₹ 114 100
Gain percent = 14%
2nd method to solve this question.
Here, r = 20%, r_{1} = 5%Gain % = r ×(100 − r_{1}) − r_{1} 100
Correct Option: C
Let C.P. be ₹ 100.
Marked price = ₹ 120S.P. = 120 × 95 = ₹ 114 100
Gain percent = 14%
2nd method to solve this question.
Here, r = 20%, r_{1} = 5%Gain % = r ×(100 − r_{1}) − r_{1} 100 Gain % = 20 × (100 − 5) − 5 100
Required Gain % = 19 – 5 = 14%
 A merchant marks his goods 40% above the cost price and sells them at a discount of 15%. Find his gain %.

 25%
 22%
 19%
 20%

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Let the C.P. of each article be ₹ 100.
∴ Marked price = ₹ 140∴ S.P. = 140 × 85 = ₹ 119 100
∴ Gain percent = 19%
2nd method to solve this question.
Here, r = 40%, r_{1} = 15%Gain % = r ×(100 − r_{1}) − r_{1} 100
Correct Option: D
Let the C.P. of each article be ₹ 100.
∴ Marked price = ₹ 140∴ S.P. = 140 × 85 = ₹ 119 100
∴ Gain percent = 19%
2nd method to solve this question.
Here, r = 40%, r_{1} = 15%Gain % = r ×(100 − r_{1}) − r_{1} 100 Gain % = 40 × (100 − 15) − 15 100 Gain % = 40 × 85 − 15 100 Gain % = 3400 − 15 100
Required Gain % = 19%
 Maha Bazaar offers 20% discount on bags which have been marked 50% above the cost price. Amarnath pays ₹ 840 for a bag. Then the cost price of the bag is

 ₹ 672
 ₹ 700
 ₹ 790
 ₹ 810

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Let the cost price be ₹ 100.
∴ Marked price = ₹ 150S.P. = 150 × 80 = ₹ 120 100
when S.P. = 120, C.P. = 100
when S.P. = 840C.P. = 100 × 840 = ₹ 700 120
2nd method to solve this question.
Here, r = 50%, r_{1} = 20%,
S.P. = ₹ 840Gain % = r ×(100 − r_{1}) − r_{1} 100
Correct Option: B
Let the cost price be ₹ 100.
∴ Marked price = ₹ 150S.P. = 150 × 80 = ₹ 120 100
when S.P. = 120, C.P. = 100
when S.P. = 840C.P. = 100 × 840 = ₹ 700 120
2nd method to solve this question.
Here, r = 50%, r_{1} = 20%,
S.P. = ₹ 840Gain % = r ×(100 − r_{1}) − r_{1} 100 Gain % = 50 × (100 − 20) − 20 100 Gain % = 50 × 80 − 20 100
Gain % = 20%
We know that ,Gain % = S.P. − C.P. × 100 C.P. 20 = 840 − p × 100 p
20p= 84000 – 100p
120p = 84000
p = 700
∴ C.P. = ₹ 700
 A trader marks his goods 40% above cost price and allows a discount of 25 %. The profit he makes, is :

 15%
 10 %
 5 %
 2 %

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Let the cost price be ₹ 100.
Marked price = ₹ 140S.P.= 75 × 140 = ₹ 105 100
∴ Profit percent = 5%
2nd method to solve this question.
Here, r = 40%, r_{1} = 25%Profit % = r ×(100 − r_{1}) − r_{1} 100
Correct Option: C
Let the cost price be ₹ 100.
Marked price = ₹ 140S.P.= 75 × 140 = ₹ 105 100
∴ Profit percent = 5%
2nd method to solve this question.
Here, r = 40%, r_{1} = 25%Profit % = r ×(100 − r_{1}) − r_{1} 100 = 40 × (100 − 25) − 25 100 = 40 × 75 − 25 100 = 3000 − 25 100
Profit % = 30 – 25 = 5%