## Discount

#### Discount

1. A reduction of 20% in the price of rice enables a customer to purchase 12.5 kg more for ₹ 800. The original price of rice (per kg) is
1. ₹ 14
2. ₹ 16
3. ₹ 12
4. ₹ 15

1. Let original price of rice = x /kg

 New price = 4x per kg 5

 ∴ 800 − 800 = 12.5 4x/5 x

 ⇒  800 5 − 1 = 12.5 4x x

 ⇒  800 5 − 4 = 12.5 4x

 ⇒ 800 = 12.5 4x

 ⇒  x = 200 = ₹ 16/kg 12.5

##### Correct Option: B

Let original price of rice = x /kg

 New price = 4x per kg 5

 ∴ 800 − 800 = 12.5 4x/5 x

 ⇒  800 5 − 1 = 12.5 4x x

 ⇒  800 5 − 4 = 12.5 4x

 ⇒ 800 = 12.5 4x

 ⇒  x = 200 = ₹ 16/kg 12.5

1. A mobile phone is listed at ₹ 1,500 and a discount of 10% is offered on the list price. What additional discount must be offered to the customer now to bring the net price to ₹ 1,242?
1. 10%
2. 8%
3. 12%
4. 18%

1.  Price after discount of 10%= 1500 × 90 = ₹ 1350 100

Second discount
= 1350 – 1242 = ₹ 108
If the rate of second discount be x% then,
 1350 × x = 108 100

 ⇒  x = 108 × 100 = 8% 1350

##### Correct Option: B

 Price after discount of 10%= 1500 × 90 = ₹ 1350 100

Second discount
= 1350 – 1242 = ₹ 108
If the rate of second discount be x% then,
 1350 × x = 108 100

 ⇒  x = 108 × 100 = 8% 1350

1. The interest on a certain sum of money is ₹ 22 and the true discount on the same sum for the same time and at the same rate is ₹ 20, Find the sum.
1. ₹ 220
2. ₹ 200
3. ₹ 210
4. ₹ 212

1.  Sum = S.I. × True discount S.I. − True discount

 = 22 × 20 = ₹ 220 22 − 20

##### Correct Option: A

 Sum = S.I. × True discount S.I. − True discount

 = 22 × 20 = ₹ 220 22 − 20

1. A shop offers 10% discount on every purchase of an article. It also offers an additional discount of 12%, if the payment is made in cash. If the original price of an item is ₹ 250, how much a customer will pay, if he wants to pay the price in cash?
1. ₹ 180
2. ₹ 192
3. ₹ 198
4. ₹ 195

1.  Required S.P. = 250 × 90 × 88 = ₹ 198 100 100

##### Correct Option: C

 Required S.P. = 250 × 90 × 88 = ₹ 198 100 100

1. The cost of manufacture of a tape recorder is ₹ 1,500. The manufacturer fixes the marked price 20% above the cost of manufacture and allows a discount in such a way as to get a profit of 8%. The rate of discount is
1. 12%
2. 8%
3. 20%
4. 10%

1.  Marked price of tape recorder = 1500 × 120 = ₹ 1800 100

 Gain = 1500 × 8 = ₹ 120 100

Discount = 1800 – (1500 + 120) = ₹ 180
Let Discount percent = d%, then
 1800 × d = 180 ⇒ d = 10% 100

Second Method to solve this question :
If the discount be y%, then
 20 − y − 20y = 8 100

 ⇒  20 − 6y = 8 5

##### Correct Option: D

 Marked price of tape recorder = 1500 × 120 = ₹ 1800 100

 Gain = 1500 × 8 = ₹ 120 100

Discount = 1800 – (1500 + 120) = ₹ 180
Let Discount percent = d%, then
 1800 × d = 180 ⇒ d = 10% 100

Second Method to solve this question :
If the discount be y%, then
 20 − y − 20y = 8 100

 ⇒  20 − 6y = 8 5

 ⇒ 6y = 20 − 8 = 12 5

 ⇒  y = 12 × 5 = 10% 6