## Discount

#### Discount

1. If the cost of an article is Rs. P after two successive reductions of 20% and 25%, the original price of the article was
1.  Rs. 5P 3
2.  Rs. 4P 5
3.  Rs. 3P 5
4.  Rs. 5P 4

1. Let us assume the price of article = Rs. A
According to the question,

 P = A x (100 − 20) × 100 − 25 100 100

 ⇒ P = A × 80 × 75 100 100

##### Correct Option: A

Let us assume the price of article = Rs. A
According to the question,

 P = A x (100 − 20) × 100 − 25 100 100

 ⇒ P = A × 80 × 75 100 100

 ⇒ P = A × 4 × 3 = 3A 5 4 5

 ⇒  A = Rs. 5 P 3

1. A dealer buys a table listed at Rs. 1,500 and gets successive discounts of 20% and 10%. He spends Rs. 20 on transportation and sells it at a profit of 20%. Find the selling price of the table.
1. Rs. 1,420
2. Rs. 1,300
3. Rs. 1,320
4. Rs. 1,380

1. Single equivalent discount for 20% and 10%

 = 20 + 10 − 20 × 10 % = 28% 100

∴  C.P. = (100 – 28)% of 1500
 ∴  C.P = 1500 × 72 = Rs. 1080 100

Actual C.P. = Rs. (1080 + 20) = Rs. 1100

##### Correct Option: C

Single equivalent discount for 20% and 10%

 = 20 + 10 − 20 × 10 % = 28% 100

∴  C.P. = (100 – 28)% of 1500
 ∴  C.P = 1500 × 72 = Rs. 1080 100

Actual C.P. = Rs. (1080 + 20) = Rs. 1100

 ∴  S.P. on 20% profit = 1100 × 120 = Rs. 1320 100

1. Allowing 20 % and 15 % successive discounts, the selling price of an article becomes Rs. 3,060; then the marked price will be
1. Rs. 4,000
2. Rs. 4,400
3. Rs. 5,000
4. Rs. 4,500

1. Let us assume the Marked price of article = Rs. M
According to the question,

 M × 80 × 85 = 3060 100 100

Alternate method to solve this question :

According to given question.
Here, S.P. = Rs. 3060, M.P. = ?, D1 = 20%, D2 = 15%

 S.P = M.P 100 − D1  100 − D2 100 100
 3060 = M.P. 100 − 20  100 − 15 100 100

##### Correct Option: D

Let us assume the Marked price of article = Rs. M
According to the question,

 M × 80 × 85 = 3060 100 100

 ⇒  M = 3060 × 100 × 100 80 × 85

M = Rs. 4500
Alternate method to solve this question :
According to given question.
Here, S.P. = Rs. 3060, M.P. = ?, D1 = 20%, D2 = 15%

 S.P = M.P 100 − D1  100 − D2 100 100

 3060 = M.P. 100 − 20  100 − 15 100 100
 3060 = M.P. 80 × 85 100 100

 M.P. = 3060 × 10000 80 × 85

M.P. = Rs. 4500

1. The difference between a discount of 30% and two successive discounts of 20% and 10% on the marked price of an article is Rs. 144. The marked price of the article is
1. Rs. 7,200
2. Rs. 7,400
3. Rs. 7,500
4. Rs. 7,000

1. Let the marked price of article be Rs. M.

 Single equivalent discount for X % and Y % = x + y − xy % 100

 Single equivalent discount for 20% and 10% = 20 + 10 − 20 × 10 % = 28% 100

According to the question,

30% of M – 28% of M = 144
Solve this equation further to calculate the Marked price of the article.

##### Correct Option: A

Let the marked price of article be Rs. M.

 Single equivalent discount for X % and Y % = x + y − xy % 100

 Single equivalent discount for 20% and 10% = 20 + 10 − 20 × 10 % = 28% 100

According to the question,

30% of M – 28% of M = 144
 ⇒ M × 2 = 144 100

 ⇒  M = 144 × 100 2

⇒  M = Rs. 7200

1. An article is marked at ₹ 5,000. The shopkeeper allows successive discounts of x%, y%, z% on it. The net selling price is
1.  ₹ (100 − x)(100 + y)(100 + z) 200
2.  ₹ (100 + x)(100 + y)(100 − z) 200
3.  ₹ (100 − x)(100 − y)(100 − z) 200
4.  ₹ (100 − x)(100 + y)(100 − z) 200

1.  Required S.P = 5000 × (100 − x) × (100 − y) × (100 − z) 100 100 100

##### Correct Option: C

 Required S.P = 5000 × (100 − x) × (100 − y) × (100 − z) 100 100 100

 Required S.P = ₹ (100 − x)(100 − y)(100 − z) 200