## Discount

#### Discount

1. A pen is listed for ₹ 12. A discount of 15% is given on it. A second discount is given bringing the price down to ₹ 8.16. The rate of second discount is
1. 20%
2. 15%
3. 18%
4. 25%

1. Let the rate of second discount be x %
After 15% discount,

 Price of pen = 85 × 12 = ₹ 10.20 100

Now, 10.20 – 8.16 = ₹ 2.04
It is second discount.
 ∴ x ×10.20 = 2.04 100

⇒  10.2x = 204
 ⇒ x = 204 = 20% 10.2

##### Correct Option: A

Let the rate of second discount be x %
After 15% discount,

 Price of pen = 85 × 12 = ₹ 10.20 100

Now, 10.20 – 8.16 = ₹ 2.04
It is second discount.
 ∴ x ×10.20 = 2.04 100

⇒  10.2x = 204
 ⇒ x = 204 = 20% 10.2

1. The marked price of a toy is ₹ 60 and at a discount that was sold for ₹ 45. Then rate of discount allowed is
1. 30%
2. 35%
3. 20%
4. 25%

1. If the rate of discount be x%, then

 60 × x = 60 − 45 = 15 100

 ⇒  x = 15 × 100 = 25% 60

Second Method :
M.P. = ₹ 60
S.P. = ₹ 5
 Discount % = M.P. − S.P. × 100 M.P.

 Discount % = 60 − 45 × 100 60

 = 15 × 100 = 25% 60

##### Correct Option: D

If the rate of discount be x%, then

 60 × x = 60 − 45 = 15 100

 ⇒  x = 15 × 100 = 25% 60

Second Method :
M.P. = ₹ 60
S.P. = ₹ 5
 Discount % = M.P. − S.P. × 100 M.P.

 Discount % = 60 − 45 × 100 60

 = 15 × 100 = 25% 60

1. A toy train is marked at ₹ 400 and sold at a discount of 8% during Ganesh puja. A shopkeeper announces a discount of 8%. The amount he will loose if he announces a single discount of 16% is
1. ₹ 2.56
2. ₹ 3.84
3. ₹ 4.16
4. ₹ 5.78

1. Single equivalent discount for successive discounts of 8% and 8%

 = 8 + 8 − 8 × 8 % 100

= (16 − 0.64)%
∴  Difference = 0.64%
∴  Loss = 400 × 0.64%
 Amount he will losse = 400 × 64 = ₹ 2.56 100 × 100

##### Correct Option: A

Single equivalent discount for successive discounts of 8% and 8%

 = 8 + 8 − 8 × 8 % 100

= (16 − 0.64)%
∴  Difference = 0.64%
∴  Loss = 400 × 0.64%
 Amount he will losse = 400 × 64 = ₹ 2.56 100 × 100

1. For a certain article, if discount is 25% the profit is 25%. If the discount is 10%, then the profit is
1. 50%
2. 40%
3. 30%
4.  33 1 % 3

1. Let the marked price be x and cost price be 100, then

 x × 75 = 125 100

 ⇒  x = 125 × 100 = ₹ 500 75 3

 S.P. after a discount of 10% = 500 × 90 = ₹ 150 3 100

∴  Gain per cent = 50%
Second Method :Here, r = 25%, D = 25%.
 M.P. = 100 + 25 C.P. 100 − 25

 M.P. = 125 = 5 C.P. 75 3

Now, D =10%
Profit = ?
 M.P. = 100 + r C.P. 100 − D

 5 = 100 + r 3 100 − D

 100 + r = 5 × 90 3

r = 150 – 100
r = 50%

##### Correct Option: A

Let the marked price be x and cost price be 100, then

 x × 75 = 125 100

 ⇒  x = 125 × 100 = ₹ 500 75 3

 S.P. after a discount of 10% = 500 × 90 = ₹ 150 3 100

∴  Gain per cent = 50%
Second Method :Here, r = 25%, D = 25%.
 M.P. = 100 + 25 C.P. 100 − 25

 M.P. = 125 = 5 C.P. 75 3

Now, D =10%
Profit = ?
 M.P. = 100 + r C.P. 100 − D

 5 = 100 + r 3 100 − D

 100 + r = 5 × 90 3

r = 150 – 100
r = 50%

1. A reduction of 10% in the price of a commodity enables a person to buy 25 kg more for ₹ 225. The original price of the commodity per kg was
1. ₹ 2
2. ₹ 1
3. ₹ 2.50
4. ₹ 1.50

1. Original price of article be x/kg.

 New price = 9x /kg. 10

 ∴ 225 − 225 = 25 9x/10 x

 ⇒ 225 × 10 − 225 = 25 9x x

 ⇒ 250 − 225 = 25 x x

 ⇒ 25 = 25 ⇒ x = ₹ 1/kg. x

##### Correct Option: B

Original price of article be x/kg.

 New price = 9x /kg. 10

 ∴ 225 − 225 = 25 9x/10 x

 ⇒ 225 × 10 − 225 = 25 9x x

 ⇒ 250 − 225 = 25 x x

 ⇒ 25 = 25 ⇒ x = ₹ 1/kg. x