## Discount

#### Discount

1. A bicycle, marked at ₹ 2,000, is sold with two successive discount of 20% and 10%. An additional discount of 5% is offered for cash payment. The selling price of the bicycle at cash payment is
1. ₹ 1,368
2. ₹ 1,468
3. ₹ 1,568
4. ₹ 1,668

1. Single equivalent discount for two successive discounts of 20% and 10%

 = 28 + 10 − 20 × 10 % = 28% 100

Now , single discount for 28% and 5%
 = 28 + 5 − 28 × 5 % 100

= (33 – 1.4) % = 31.6%
∴  Required selling price of bicycle at cash payment = (100 – 31.6) % of ₹ 2000

##### Correct Option: A

Single equivalent discount for two successive discounts of 20% and 10%

 = 28 + 10 − 20 × 10 % = 28% 100

Now , single discount for 28% and 5%
 = 28 + 5 − 28 × 5 % 100

= (33 – 1.4) % = 31.6%
∴  Required selling price of bicycle at cash payment = (100 – 31.6) % of ₹ 2000
 ∴  Required selling price of bicycle at cash payment = 2000 × 68.4 = ₹ 1368 100

1. An article listed at ₹ 800 is sold at successive discounts of 25% and 15%. The buyer desires to sell it off at a profit of 20% after allowing a 10% discount. What would be his list price ?
1. ₹ 620
2. ₹ 600
3. ₹ 640
4. ₹ 680

1. Effective discount

 = 25 + 15 − 25 × 15 100

= 40 – 3.75 = 36.25 %
∴  CP for buyer = (100 – 36.25) % of 800
 = 63.75 × 800 = ₹ 510 100

∴  To gain 20%,
 SP = ₹ 120 × 510 = ₹ 612 100

Let the list price be ₹ P.
∴  90% of P = ₹ 612

##### Correct Option: D

Effective discount

 = 25 + 15 − 25 × 15 100

= 40 – 3.75 = 36.25 %
∴  CP for buyer = (100 – 36.25) % of 800
 = 63.75 × 800 = ₹ 510 100

∴  To gain 20%,
 SP = ₹ 120 × 510 = ₹ 612 100

Let the list price be ₹ P.
∴  90% of P = ₹ 612
 ⇒ 90P = 612 ⇒ P = 61200 100 90

= ₹ 680

1. A dealer buys a car listed at ₹ 200000 at successive discounts of 5% and 10%. If he sells the car for 179550, then his profit is
1. 10%
2. 9%
3. 5%
4. 4%

1. As we know the formula for Equivalent discount for two successive discount.

 Equivalent discount =   10 + 5 − 10 × 5 = 14.5% 100

Alternate method to solve this question :
According to given question, Marked Price = 200000, Selling Price is Cost Price for Buyer.
D1 = 5%,
D2 = 10%
 Selling Price = Marked Price 100 − D1  100 − D2 100 100

 = 200000 100 − 5  100 − 10 100 100

##### Correct Option: C

As we know the formula for Equivalent discount for two successive discount.

 Equivalent discount =   10 + 5 − 10 × 5 = 14.5% 100

∴  C P (for buyer) = 85.5% of ₹ 200000
 = ₹ 85.5 × 200000 = ₹ 171000 100

Selling Price = ₹ 179550
Profit = ₹ (179550 – 171000) = ₹ 8550
 ∴  Gain % = 8550 × 100 = 5% 171000

Alternate method to solve this question :
Here, Marked Price = 200000, Selling Price is Cost Price for buyer.
D1 = 5%,
D2 = 10%
 Selling Price = Marked Price 100 − D1  100 − D2 100 100

 = 200000 100 − 5  100 − 10 100 100

= 20 × 95 × 90 = 1800 x 95
Cost Price for buyer = 171000
Selling Price for buyer = 179550
 Profit = Selling Price − Cost Price × 100% C.P.

 = 8550 × 100 = 5% 171000

1. A shopkeeper gives two successive discounts on an article marked ₹ 450. The first discount given is 10 percent. If the customer pays ₹ 344.25 for the article, the second discount given is
1. 14 %
2. 10 %
3. 12 %
4. 15 %

1. Let the second discount be D2 %.
According to the question,

 344.25 = 450 × 100 − 10 × 100 − D2 100 100

Alternate method to solve this question :
Here, M.P. = Rs. 450, S.P. = Rs. 344.25, D1 = 10%, D2 = ?
 S.P. = M.P. 100 − D1  100 − D2 100 100

 344.25 = 450 × 100 − 10  100 − D2 100 100

##### Correct Option: D

Let the second discount be D2 %.
According to the question,

 344.25 = 450 × 100 − 10 × 100 − D2 100 100

 ∴  100 − D2 = 344.25 × 100 × 100 450 × 90

∴  100 – D2 = 85
∴  D2 = 100 – 85 = 15%.
Alternate method to solve this question :
Here, M.P. = Rs. 450, S.P. = Rs. 344.25, D1 = 10%, D2 = ?
 S.P. = M.P. 100 − D1  100 − D2 100 100

 344.25 = 450 × 100 − 10  100 − D2 100 100

 3442500 = (100 − D2) 450 × 90

 34425 = (100 − D2) 45 × 9

 3825 = (100 − D2) 45 × 1

 425 = (100 − D2) 5 × 1

⇒  85 = 100 – D2
⇒  D2 = 15 %

1. A person paid ₹ 17,000 for a motor-car after a single discount of 15%. If he is given successive discounts of 5% and 10% then how much he would pay ?
1. ₹ 17,000
2. ₹ 17,010
3. ₹ 17,100
4. ₹ 18,900

1. Let M be the marked price.
Single Discount = 15%
⇒  100 – 15 = 85 %
85% of M = 17,000

 Required SP = 20,000 × 95 × 90 100 100

Alternate method to solve this question :
 M.P = S.P. × 100 100 − D

 M.P = 17000 × 100 100 − 15

 M.P = 17000 × 100 85

##### Correct Option: C

Let M be the marked price.
Single Discount = 15%
⇒  100 – 15 = 85
85% of M = 17,000

 ∴  M = 17,000 × 100 85

M = ₹ 20,000
 Required SP = 20,000 × 95 × 90 100 100

Required SP = 180 × 95 = ₹ 17100
Alternate method to solve this question :
 M.P = S.P. × 100 100 − D

 M.P = 17000 × 100 100 − 15

 M.P = 17000 × 100 85

M.P. = 20000

 S.P = M.P. 100 − D1  100 − D2 100 100

 S.P = 20000 100 − 5  100 − 10 100 100

 S. P = 20000 × 95 × 90 100 100

S.P = 180 × 95 = ₹ 17100