## Discount

#### Discount

1. The marked price of watch was ₹ 820. A man bought the watch for ₹ 570.72 after getting two successive discounts, of which the first was 20%. The second discount was
1. 18%
2. 15%
3. 13%
4. 11%

1. Total discount = ₹ (820 – 570.72) = ₹ 249.28

 First discount = 820 × 20 = ₹ 164 100

∴  Second discount = ₹ (249.28 – 164) = ₹ 85.28
Price of the article after first discount = ₹ (820 – 164) = ₹ 656
If the second discount be D2 % ,
then D2 % of 656 = 85.28

Alternate method to solve this question :
Here, M.P. = Rs. 820, S.P. = 570.72, D1 = 20%, D2 = ?
 S.P. = M.P. 100 − D1  100 − D2 100 100

##### Correct Option: C

Total discount = ₹ (820 – 570.72) = ₹ 249.28

 First discount = 820 × 20 = ₹ 164 100

∴  Second discount = ₹ (249.28 – 164) = ₹ 85.28
Price of the article after first discount = ₹ (820 – 164) = ₹ 656
If the second discount be D2 % ,
then D2 % of 656 = 85.28
 ⇒  D2 = 85.28 × 100 = 13% 656

Alternate method to solve this question :
Here, M.P. = Rs. 820, S.P. = 570.72, D1 = 20%, D2 = ?
 S.P. = M.P. 100 − D1  100 − D2 100 100

 570.72 = 820 100 − 20  100 − D2 100 100

 5707200 = 100 − D2 820 × 80

100 − D2 = 87
D2 = 13 %

1. An article is listed at ₹ 920. A customer pays ₹ 742.90 for it after getting two successive discounts. If the rate of first discount is 15%, the rate of 2nd discount is
1. 3%
2. 5%
3. 8%
4. 12%

1. Total discount = ₹ (920 – 742.90) = ₹ 177.10
First discount = 15%
∴  Discount = 15% of 920

 = 920 × 15 = ₹ 138 100

Price after this discount = 920 – 138 = ₹ 782
Remaining discount = 177.10 – 138 = ₹ 39.10
Let the second discount be D2 %.
 ∴ 782 × D2 = 39.10 100

Alternate method to solve this question :
Here, M.P. = Rs. 920, S.P. = Rs. 742.90
D1 = 15%, D2 = ?
 S.P. = M.P. 100 − D1  100 − D2 100 100

 742.90 = 920 100 − 15  100 − D2 100 100

##### Correct Option: B

Total discount = ₹ (920 – 742.90) = ₹ 177.10
First discount = 15%
∴  Discount = 15% of 920

 = 920 × 15 = ₹ 138 100

Price after this discount = 920 – 138 = ₹ 782
Remaining discount = 177.10 – 138 = ₹ 39.10
Let the second discount be D2 %.
 ∴ 782 × D2 = 39.10 100

 ⇒  D2 = 39.10 × 100 = 5% 782

Alternate method to solve this question :
Here, M.P. = Rs. 920, S.P. = Rs. 742.90
D1 = 15%, D2 = ?
 S.P. = M.P. 100 − D1  100 − D2 100 100

 742.90 = 920 100 − 15  100 − D2 100 100

 7429000 = 100 − D2 920 × 85

95 = 100 – D2
⇒   D2 = 5%

1. The difference between a discount of 40% on ₹ 500 and two successive discounts of 36 % and 4 % on the same amount is
1. zero
2. ₹ 1.93
3. ₹ 2.00
4. ₹ 7.20

1. As we know the formula for a equivalent discount for two success discounts.
Single equivalent discount of two successive discounts of 36% and 4%.

 = 36 + 4 − 36 × 4 100

= 40 – 1.44 = 38.56
Percentage difference = 40 – 38.56 = 1.44

##### Correct Option: D

As we know the formula for a equivalent discount for two success discounts.
Single equivalent discount of two successive discounts of 36% and 4%.

 = 36 + 4 − 36 × 4 100

= 40 – 1.44 = 38.56
Percentage difference = 40 – 38.56 = 1.44

 ∴  Required difference = 500 × 1.44 = ₹ 7.20 100

1. An article is listed at ₹ 900 and two successive discounts of 8% and 8% are given on it. How much would the seller gain or lose, if he gives a single discount of 16%, instead of two discounts ?
1. Gain of ₹ 4.76
2. Loss of ₹ 5.76
3. Gain of ₹ 5.76
4. Loss of ₹ 4.76

1. As we know the formula for a equivalent discount for two successive discount.
Equivalent discount for two successive discounts of 8% and 8%

 = 8 + 8 − 8 × 8 % 100

For a single discount of 16%,
SP = 84 % of 900

##### Correct Option: B

As we know the formula for a equivalent discount for two successive discount.
Equivalent discount for two successive discounts of 8% and 8%

 = 8 + 8 − 8 × 8 % 100

= (16–0.64) % = 15.36 %
∴  SP = (100 –15.36) % of 900
 = ₹ 84.64 × 900 = ₹ 761.76 100

For a single discount of 16%,
SP = 84% of 900
 = ₹ 84 × 900 = ₹ 756 100

Certainly seller will lose in this case.
∴  Loss = ₹ (761.76 – 756)
= ₹ 5.76

1. The list price of a clock is ₹ 160. A customer buys it for ₹ 122.40 after two successive discounts. If first discount is 10%, the second is
1. 10%
2. 12%
3. 15%
4. 18%

1. As per given question marked price = 160
After 10% discount, The Selling price

 S.P. = 100 - 10 × 160 = ₹ 144 100

Let us assume the other discount = D%
 ∴ (100 − D) × 144 = ₹ 122.40 100

 ⇒  100 − D = 12240 144

Alternate method to solve this question :
 S.P. = M.P. 100 − D1  100 − D2 100 100

##### Correct Option: C

As per given question marked price = 160
After 10% discount, The Selling price

 S.P. = 100 - 10 × 160 = ₹ 144 100

Let us assume the other discount = D%
 ∴ (100 − D) × 144 = ₹ 122.40 100

 ⇒  100 − D = 12240 144

⇒  100 – D = 85
⇒  D = 100 – 85 = 15%
Alternate method to solve this question :
 S.P. = M.P. 100 − D1  100 − D2 100 100

 ⇒  122.40 = 160 100 − 10  100 − D2 100 100

 12240 = 90 × 100 - D2 160 100

 1224000 = 100 − D2 160 × 90

 12240 = 100 − D2 16 × 9

 1360 = 100 − D2 16 × 1

⇒  85 = 100 – D2
⇒  D2 = 15%