True Discount
- The true discount on a bill of $ 1260 is due for 6 months at 10 % per annum is:
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Given :- Amount = $ 1260 , Time = 6 months = 0.5 years , Rate = 10%
∴ True Discount = $ Amount x Rate x Time 100 + ( Rate x Time )
Correct Option: A
Given :- Amount = $ 1260 , Time = 6 months = 0.5 years , Rate = 10%
∴ True Discount = $ Amount x Rate x Time 100 + ( Rate x Time ) True Discount = $ 1260 x 0.5 x 10 = $ 60 . 100 + ( 0.5 x 10 )
- 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 $ x
Therefore, in case 1,Selling Price ( SP1 ) = $ 70x % 100
Single discount equivalent to successive discounts of 20% and 10%.
Here , a = 20% and b = 10%Equivalent discount = 
a + b - a x b 
%100 Equivalent discount = 20 + 10 - 20 x 10 %100
= ( 30 - 2 ) % = 28%In case 2 ,Selling Price ( SP2 ) = $ 72x 100 Correct Option: A
Let the marked price be $ x
Therefore, in case 1,Selling Price ( SP1 ) = $ 70x % 100
Single discount equivalent to successive discounts of 20% and 10%.
Here , a = 20% and b = 10%Equivalent discount = a + b - a x b %100 Equivalent discount = 20 + 10 - 20 x 10 %100
= ( 30 - 2 ) % = 28%In the case 2 , Selling Price ( SP2 ) = $ 72x 100
Therefore, SP2 - SP1$ 72x - 70x = $ 72 100 100 ⇒ 2x = 72 100
⇒ 2x = 7200⇒ x = 7200 2
x = $ 3600
Hence , the marked price is $ 3600 .
- A fan is listed at $ 1500 and a discount of 20% is offered on the list price. What additional discount must be offered to the customer to bring the net price to $ 1104?
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Let Additional discount = D %
Given :- Marked Price ( M.P. ) = $ 1500
Discount = 20%
∴ Selling Price ( S.P. ) = $ 1200Correct Option: A
Let Additional discount = D %
Given :- Marked Price ( M.P. ) = $ 1500
Discount = 20%
∴ Selling Price ( S.P. ) = $ 1200
Let, 1200 - D % of 1200 = $ 1104
⇒ D % of 1200 = 1200 - 1104 = 96D × 1200 = 96 ⇒ D = 8 100
∴ An additional discount of 8% must be offered to the customer to bring the net price to $ 1104.
- An article is marked 40 % above the cost price and a discount of 30 % is allowed. What is the gain or loss % ?
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Let the Cost Price ( C.P. ) of the article be $ 100.
Therefore, marked price = $ 140
Selling Price ( S.P. ) = 70% of 140 = $ 98
Loss = Cost Price - Selling Price = 100 - 98 = $ 2∴ Loss% = Loss x 100% Cost Price Correct Option: C
Let the Cost Price ( C.P. ) of the article be $ 100.
Therefore, marked price = $ 140
Selling Price ( S.P. ) = 70% of 140 = $ 98
Loss = Cost Price - Selling Price = 100 - 98 = $ 2∴ Loss% = Loss x 100% Cost Price loss % = 2 x 100 = 2 % 100
- $ 21 is the true discount on $ 371 for a certain time at certain int. If the rate of interest is kept same, true discount on the same sum for double that time will be :
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Given that , Amount = $ 371 , True discount = $ 21
∴ Present worth = Amount - True discount
Present worth = $ (371 - 21) = $ 350
Also, True discount = Simple Interest on Present worth
∴ Simple Interest on $ 350 for a certain period at certain rate p.c. = $ 21.
∴ Simple Interest on $ 350 for double the period at same rate p.c. = $ 42.
∴ $ 42 is True discount on $ (350 + 42) = $ 392 for double the period.
∴ T.D. on $ 371 for double the period and same rate p.c.Correct Option: B
Given that , Amount = $ 371 , True discount = $ 21
∴ Present worth = Amount - True discount
Present worth = $ (371 - 21) = $ 350
Also, True discount = Simple Interest on Present worth
∴ Simple Interest on $ 350 for a certain period at certain rate p.c. = $ 21.
∴ Simple Interest on $ 350 for double the period at same rate p.c. = $ 42.
∴ $ 42 is True discount on $ (350 + 42) = $ 392 for double the period.
∴ T.D. on $ 371 for double the period and same rate p.c.True discount = 42 x 371 = $ 39.75 392
