## Discount

#### Discount

1. 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%

1. 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%

1. 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

1. 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

1. 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

1. 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.

1. 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

1. 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.

1. 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

1.  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.