Discount
- Which of the following successive discounts is better to a customer?
(a) 20%, 15%, 10% or
(b) 25%, 12%, 8% ?
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(a) Single equivalent discount for 20% and 15%
= 
20 + 15 − 20 × 15 
% = 32% 100
(b) Single equivalent discount for 25% and 12%= 25 + 12 − 25 × 12 % = 34% 100
Alternate method to solve this question :
Case I.
D1 = 20%, D2 = 15%, D3 = 10%Equivalent discount = 100 − 
100 − D1 100 − D2 100 − D3 × 100 
100 100 100
Case II.
D1 = 25%, D2 = 12%, D3 = 8%Equivalent discount = 100 − 100 − D1 100 − D2 100 − D3 × 100 100 100 100 Correct Option: B
(a) Single equivalent discount for 20% and 15%
= 20 + 15 − 20 × 15 % = 32% 100
Single equivalent discount for 32% and 10%= 32 + 10 − 32 × 10 % = 38.8% 100
(b) Single equivalent discount for 25% and 12%= 25 + 12 − 25 × 12 % = 34% 100
Single equivalent discount for 34% and 8%= 34 + 8 − 34 × 8 % = 42 – 2.72 = 39.28% 100
Alternate method to solve this question :
Case I.
D1 = 20%, D2 = 15%, D3 = 10%Equivalent discount = 100 − 100 − D1 100 − D2 100 − D3 × 100 100 100 100 Equivalent discount = 100 − 100 − 20 100 − 15 100 − 10 × 100 100 100 100 Equivalent discount = 100 − 80 × 85 × 90 × 100 100 100 100
Equivalent discount = 100 – 61.2 = 38.8%
Case II.
D1 = 25%, D2 = 12%, D3 = 8%Equivalent discount = 100 − 100 − D1 100 − D2 100 − D3 × 100 100 100 100 Equivalent discount = 100 − 100 − 25 100 − 12 100 − 8 × 100 100 100 100 Equivalent discount = 100 − 75 × 88 × 92 × 100 100 100 100
Equivalent discount = 100 – 60.72 = 39.28%
⇒ Case II is better than Case I.
- The printed price of a book is ₹ 320. A retailer pays ₹ 244.80 for it. He gets successive discounts of 10% and an another rate. His second rate is :
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First discount = 320 × 10 = ₹ 32 100
∴ Price after first discount = 320 – 32 = ₹ 288
If the second discount be D %, then∴ 288 × D = 288 − 244.80 = 43.2 100
Alternate method to solve this question :
Here, M.P. = Rs. 320, S.P. = Rs.244.80, D1 = 10%, D2 = ?S.P. = M.P. 100 − D1 100 − D2 100 100 ⇒ 244.80 = 320 100 − 10 100 − D2 100 100
Correct Option: A
First discount = 320 × 10 = ₹ 32 100
∴ Price after first discount = 320 – 32 = ₹ 288
If the second discount be D %, then∴ 288 × D = 288 − 244.80 = 43.2 100
⇒ 288 x D = 43.2 x 100⇒ D = 43.2 × 100 = 15% 288
Alternate method to solve this question :
Here, M.P. = Rs. 320, S.P. = Rs.244.80, D1 = 10%, D2 = ?S.P. = M.P. 100 − D1 100 − D2 100 100 ⇒ 244.80 = 320 100 − 10 100 − D2 100 100 2448000 = 100 − D2 320 × 90
100 − D2 = 85
⇒ D2 = 100 − 85
⇒ D2 = 15%
- The marked price of a table is ₹ 800. A retailer bought it after two successive discounts of 10 % and 15 %. He spent ₹ 13 on transportation and sold it for ₹ 875. His profit was
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C.P of the table = 800 × 90 × 85 = ₹ 612 100 100 Correct Option: A
C.P of the table = 800 × 90 × 85 = ₹ 612 100 100
Actual Cost Price = 612 + 13 = ₹ 625
Profit = 875 – 625 = ₹ 250∴ Profit % = Profit × 100 Actual Cost Price ∴ Profit % = 250 × 100 = 40% 625
- A trader allows two successive discounts of 30% and 15% on selling an article. If he gets ₹ 476 for that article, find its marked price.
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Single equivalent discount = 30 + 15 − 35 × 15 % = 40.5% 100
Alternate method to solve this question :
Here, S.P. = Rs. 476, D1 = 30%,D2 = 15%S.P. = M.P. 100 − D1 100 − D2 100 100
Correct Option: D
Single equivalent discount = 30 + 15 − 35 × 15 % = 40.5% 100
If the marked price be M, thenM × 100 × 40.5 = 476 100 ⇒ M = 476 × 100 = ₹ 800 59.5
Alternate method to solve this question :
Here, S.P. = Rs. 476, D1 = 30%,D2 = 15%S.P. = M.P. 100 − D1 100 − D2 100 100 476 = M.P. 100 − 30 100 − 15 100 100 M.P. = 4760000 70 × 85
M.P. = ₹ 800
- If on a marked price, the difference of selling prices with a discount of 30% and two successive discounts of 20% and 10% is ₹ 72, then the marked price (in rupees) is
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Let the marked price be ₹ M.
∴ In case I, Selling Price = ₹ 70M 100
Single discount equivalent to successive discounts of 20% and 10%.= 20 + 10 − 20 × 10 % = 28% 100 ∴ S.P. in this case = 72M 100
Correct Option: A
Let the marked price be ₹ M.
∴ In case I, Selling Price = ₹ 70M 100
Single discount equivalent to successive discounts of 20% and 10%.= 20 + 10 − 20 × 10 % = 28% 100 ∴ S.P. in this case = 72M 100 ∴ 72M − 70M = 72 100 100 ⇒ 2M = 72 100 ∴ M = 72 × 100 = ₹ 3600 2
