## Discount

#### Discount

1. 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 :
1. \$ 20
2. \$ 21.81
3. \$ 22
4. \$ 18.33

1. 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

1. 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
1. 15%
2. 12%
3. 14%
4. 17%

1. Let C.P. be ₹ 100.
Marked price = ₹ 120

 S.P. = 120 × 95 = ₹ 114 100

Gain percent = 14%
2nd method to solve this question.
Here, r = 20%, r1 = 5%
 Gain % = r ×(100 − r1) − r1 100

##### Correct Option: C

Let C.P. be ₹ 100.
Marked price = ₹ 120

 S.P. = 120 × 95 = ₹ 114 100

Gain percent = 14%
2nd method to solve this question.
Here, r = 20%, r1 = 5%
 Gain % = r ×(100 − r1) − r1 100

 Gain % = 20 × (100 − 5) − 5 100

Required Gain % = 19 – 5 = 14%

1. A merchant marks his goods 40% above the cost price and sells them at a discount of 15%. Find his gain %.
1. 25%
2. 22%
3. 19%
4. 20%

1. 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%, r1 = 15%
 Gain % = r ×(100 − r1) − r1 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%, r1 = 15%
 Gain % = r ×(100 − r1) − r1 100

 Gain % = 40 × (100 − 15) − 15 100

 Gain % = 40 × 85 − 15 100

 Gain % = 3400 − 15 100

Required Gain % = 19%

1. 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
1. ₹ 672
2. ₹ 700
3. ₹ 790
4. ₹ 810

1. Let the cost price be ₹ 100.
∴  Marked price = ₹ 150

 S.P. = 150 × 80 = ₹ 120 100

when S.P. = 120, C.P. = 100
when S.P. = 840
 C.P. = 100 × 840 = ₹ 700 120

2nd method to solve this question.
Here, r = 50%, r1 = 20%,
S.P. = ₹ 840
 Gain % = r ×(100 − r1) − r1 100

##### Correct Option: B

Let the cost price be ₹ 100.
∴  Marked price = ₹ 150

 S.P. = 150 × 80 = ₹ 120 100

when S.P. = 120, C.P. = 100
when S.P. = 840
 C.P. = 100 × 840 = ₹ 700 120

2nd method to solve this question.
Here, r = 50%, r1 = 20%,
S.P. = ₹ 840
 Gain % = r ×(100 − r1) − r1 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

1. A trader marks his goods 40% above cost price and allows a discount of 25 %. The profit he makes, is :
1. 15%
2. 10 %
3. 5 %
4. 2 %

1. Let the cost price be ₹ 100.
Marked price = ₹ 140

 S.P.= 75 × 140 = ₹ 105 100

∴  Profit percent = 5%
2nd method to solve this question.
Here, r = 40%, r1 = 25%
 Profit % = r ×(100 − r1) − r1 100

##### Correct Option: C

Let the cost price be ₹ 100.
Marked price = ₹ 140

 S.P.= 75 × 140 = ₹ 105 100

∴  Profit percent = 5%
2nd method to solve this question.
Here, r = 40%, r1 = 25%
 Profit % = r ×(100 − r1) − r1 100

 = 40 × (100 − 25) − 25 100

 = 40 × 75 − 25 100

 = 3000 − 25 100

Profit % = 30 – 25 = 5%