## Discount

#### Discount

1. The marked price of a watch is 800. A shopkeeper gives two successive discounts and sells the watch at 612. If the first discount is 10%, the second discount is :
1. 10%
2. 12%
3. 15%
4. 20%

1. Let the second discount be D2 %.
Then, 90 % of (100 – D2) % of 800 = 612

 ⇒ 90 × 100 − D2 × 800 = 612 100 100

Another method to solve :
Here, M.P. = Rs. 800, S.P. = Rs. 612, D1 = 10%, D2 = ?
 S.P. = M.P. 100 − D1  100 − D2 100 100

 612 = 800 × 100 − 10  100 − D2 100 100

 612 = 800 × 90 × 100 − D2 100 100

##### Correct Option: C

Let the second discount be D2 %.
Then, 90 % of (100 – D2) % of 800 = 612

 ⇒ 90 × 100 − D2 × 800 = 612 100 100

 ⇒  100 − D2 = 612 × 100 = 85 90 × 8

⇒  D2 = 100 – 85 = 15%
Another method to solve :
Here, M.P. = Rs. 800, S.P. = Rs. 612, D1 = 10%, D2 = ?
 S.P. = M.P. 100 − D1  100 − D2 100 100

 612 = 800 × 100 − 10  100 − D2 100 100

 612 = 800 × 90 × 100 − D2 100 100

 6120 = 100 × D2 72

 D2 = 100 − 6120 72

 D2 = 7200 − 6120 = 15% 72

1. The price of an article is raised by 30% and then two successive discounts of 10% each are allowed. Ultimately the price of the article is
1. increased by 10%
2. increased by 5.3%
3. decreased by 3%
4. decreased by 5.3%

1. Let us assume the original price be ₹ 100
∴  Increased price = ₹ 130

 Equivalent discount = 10 + 10 − 10 × 10 = 10 + 10 - 1 = 19 % 100

##### Correct Option: B

Let us assume the original price be ₹ 100
∴  Increased price = ₹ 130

 Equivalent discount = 10 + 10 − 10 × 10 = 10 + 10 - 1 = 19 % 100

∴  Ultimate price of the article = ( 100 - 19 )% of 130 = 81 % of 130 = 105.3
i.e. increase by 5.3%.

1. The marked price of a watch was ₹ 720. A man bought the same for ₹ 550.80, after getting two successive discounts, the first at 10 %. What was the second discount rate?
1. 12%
2. 14%
3. 15%
4. 18%

1. Marked price = ₹ 720
Actual price = ₹ 550.80
First discount D1 = 10 %
Let the second discount = D2 %
As we know the formula,

 Successive discounts of D1 % and D2 % is overall equals to = 10 + D2 − 10 × D2 % 100

 = 10 + D2 − 10 × D2 100

 = 10 + D2 − D2 10

2nd Method :
Here, Marked price = ₹ 720
Selling price = ₹ 550.80
First discount D1 = 10 %
Let assume the second discount = D2 %
As we know the formula,
 Selling Price = Market Price 100 − D1  100 − D2 100 100

 550.80 = 720 100 − 10  100 − D2 100 100

 ⇒  550.80 = 720 × 90 × 100 - D2 100 100

##### Correct Option: C

Marked price = ₹ 720
Actual price = ₹ 550.80
First discount D1 = 10 %
Let the second discount = D2 %
As we know the formula,

 Successive discounts of D1 % and D2 % is overall equals to = 10 + D2 − 10 × D2 % 100

 = 10 + D2 − 10 × D2 100

 = 10 + D2 − D2 10

= 10 + D2 - 0.1D2
= 10 + 0.9D2
According to question,
720 x ( 100 - 10 - 0.9D2) % = 550.80
⇒  720 x ( 90 - 0.9D2) = 550.80 x 100
 ⇒  90 - 0.9D2 = 55080 720

 ⇒  90 - 0.9D2 = 5508 72

 ⇒  90 - 0.9D2 = 612 8

 ⇒  0.9D2 = 90 - 612 8

 ⇒  0.9D2 = 720 - 612 8

 ⇒  0.9D2 = 108 8

 ⇒  0.9D2 = 27 2

 ⇒  D2 = 27 × 0.9 2

 ⇒  D2 = 27 × 10 × 9 2

 ⇒  D2 = 3 × 10 = 30 2 2

∴  Second discount = 15%

2nd Method to solve this question.
Here, Marked price = ₹ 720
Selling price = ₹ 550.80
First discount D1 = 10 %
Let assume the second discount = D2 %
As we know the formula,
 Selling Price = Market Price 100 − D1  100 − D2 100 100

 550.80 = 720 100 − 10  100 − D2 100 100

 ⇒  550.80 = 720 × 90 × 100 - D2 100 100

 ⇒  550.80 = 72 × 9 × 100 - D2 1 100

 ⇒  550.80 = 72 × 9 x (100 - D2) 100

⇒  550.80 x 100 = 72 × 9 x ( 100 - D2 )
⇒  55080 = 648 x ( 100 - D2 )
⇒  55080 = 648 x 100 - 648 x D2
⇒  55080 = 64800 - 648 x D2
⇒  648 x D2 = 64800 - 55080
⇒  648 x D2 = 9720
 ⇒  D2 = 9720 648

⇒  D2 = 15 %