Discount
 If a commission of 10% is given on the written price of an article, the gain is 20%. The gain per cent, when the commission is increased to 20%, will be ?

 6^{2}/_{3}%
 5%
 8%
 5^{1}/_{3}%

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Let MP of the article = ₹ N
∴ SP of the article = N x (100  10)/100 = ₹ 9N/10
⇒ CP of the article = [(9N/10) x 100]/(100 + 20)
= (9N x 10)/120
= ₹ 3N/4
Now, new SP of the article = [N x (100  20)]/100 = ₹ 4N/5
New profit = 4N/5  3N/4 = (16N  15N)/20 = ₹ N/20
Hence, profit per cent = [(N/20) / (3N/4)] x 100 %Correct Option: A
Let MP of the article = ₹ N
∴ SP of the article = N x (100  10)/100 = ₹ 9N/10
⇒ CP of the article = [(9N/10) x 100]/(100 + 20)
= (9N x 10)/120
= ₹ 3N/4
Now, new SP of the article = [N x (100  20)]/100 = ₹ 4N/5
New profit = 4N/5  3N/4 = (16N  15N)/20 = ₹ N/20
Hence, profit per cent = [(N/20) / (3N/4)] x 100 %
= (4 x 100)/(3 x 20) %
= 6^{2}/_{3}%
 If the discount on a certain sum in 2 years at a certain rate is $ 150 and the interest in 3 years is $ 240. Find the sum and the rate of interest.


$ 2400, 3 1 % 3 
$ 2400, 4 1 % 3 
$ 2200, 5 1 % 3 
$ 2000, 3 1 % 3  None of these


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Given : Interest for 3 years = $ 240.
Interest for 2 year = 240 × 2 = $160 3
Banker 's Discount = $160
Discount for 2 years = $150
True Discount = $150Sum due = Banker 's Discount × True Discount = 160 × 150 = $ 2400 Banker 's Discount  True Discount 160  150 Rate of interest = Interest × 100 % Sum due × Time Correct Option: A
Given : Interest for 3 years = $ 240.
Interest for 2 year = 240 × 2 = $160 3
Banker 's Discount = $160
Discount for 2 years = $150
True Discount = $150Sum due = Banker 's Discount × True Discount = 160 × 150 = $ 2400 Banker 's Discount  True Discount 160  150 Rate of interest = Interest × 100 % Sum due × Time Rate of interest = 240 × 100 = 3 1 % 2400 × 3 3
 A bill which being due at the end of 4 years is now worth $ 575, but if it is due in 2 years 6 months, it would now be worth $ 620. The sum of the bill is :

 $ 695
 $ 725
 $ 713
 None of these

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Let, the rate p.c. be r%.
Given : Present worth = $ 575 and Time = 4 years
Let, $ x be the amount of the bill.∴ Present worth = Amount x Rate x Time 100 + Rate x Time Then, 575 = x × 100 100 + 4r
That is, 57500 + 2300r = 100x
∴ x = 575 + 23r …(1)
Present worth = $ 620 and Time = 2 years and 6 months = 2.5 yearsand 620 = 100x 100 + 2.5 r Correct Option: C
Let, the rate p.c. be r%.
Given : Present worth = $ 575 and Time = 4 years
Let, $ x be the amount of the bill.∴ Present worth = Amount x Rate x Time 100 + Rate x Time Then, 575 = x × 100 100 + 4r
That is, 57500 + 2300r = 100x
∴ x = 575 + 23r …(1)
Present worth = $ 620 and Time = 2 years and 6 months = 2.5 yearsand 620 = 100x 100 + 2.5 r
∴ 62000 + 1550r = 100x
∴ 6200 + 155r = 10x = 5750 + 230r [using (1)]
∴ 75r = 450
∴ r = 6
Putting the value of x in eq. (1) ⇒ x = 575 + 138 = $ 713.
Hence , The sum of the bill is $ 713.
 Find the present worth (P.W.) and the true discount reckoning 6 % per annum simple interest of $ 176 due in 20 months time.

 $ 160, $ 16
 $ 130, $ 46
 $ 150, $ 26
 None of these

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Here , simple interest = $ 176 , Rate = 6% , Time = 20 months = ( 20/12 ) years
∴ Present worth = Simple interest x Rate x Time 100 + Rate x Time Present worth = 100 x 76 100 + [ 2 x ( 20/12 ) ] Correct Option: A
Here , simple interest = $ 176 , Rate = 6% , Time = 20 months = ( 20/12 ) years
Present worth = 100 x 76 100 + [ 2 x ( 20/12 ) ] Present worth = 100 x 76 = $ 160 100 + 10
True discount = Amount  Present worth
True discount = $ 176  $ 160 = $ 16.
 The discount on $ 5229 due in 1 year 9 months reckoning compound interest at 5 % is :

 $ 429.00
 $ 415.00
 $ 393.25
 None of these

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P.W = 5229 [(1 + 5 / 100)][1 + (3 / 4)(5 / 100)]
Correct Option: A
P.W = 5229 [(1 + 5 / 100)][1 + (3 / 4)(5 / 100)] = 5229 x 20 x 80 = $ 4800 21 83
∴ T.D. = $ (5229  4800) = $ 429.