Discount Difficult Questions and Answers | Page - 3

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 ?

1. 6²/₃%
2. 5%
3. 8%
4. 5¹/₃%

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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) %
= 6²/₃%

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.

1. $ 2400, 3 1 %
  3
2. $ 2400, 4 1 %
  3
3. $ 2200, 5 1 %
  3
4. $ 2000, 3 1 %
  3
5. 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 = $150

Sum 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 = $150

Sum 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 :

1. $ 695
2. $ 725
3. $ 713
4. 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 years
and 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 years
and 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.

1. $ 160, $ 16
2. $ 130, $ 46
3. $ 150, $ 26
4. 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 :

1. $ 429.00
2. $ 415.00
3. $ 393.25
4. 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.