## Discount

#### Discount

1. The present worth of a sum of money due for 146 days at 5 % is ₹400. The sum due is :
1. ₹410
2. ₹408
3. ₹415
4. ₹450
5. None of these

1. Given :- Present worth = ₹400 , Rate = 5%

 Time = 146 days = 146 years 365

 True Discount = P.W. × Time × Rate 100

##### Correct Option: B

Given :- Present worth = ₹400 , Rate = 5%

 Time = 146 days = 146 years 365

 True Discount = P.W. × Time × Rate 100

 True Discount = ₹400 × 146 × 5 = ₹8 365 100

Sum due = Present worth + True Discount
Sum due = ₹400 + ₹8 = ₹408.

1. A banker discounts a 4 months bill at 3 %. If the proceeds be invested in a manner, so that nothing is lost, the interest rate should be :
1. 3%
2. 4%
3.  3 1 % 33
4.  3 1 % 36
5. None of these

1.  Here , 4 months = 1 years 3
 & there4; Banker deducts ₹3 × 1 = ₹1 from a bill of ₹100 3

Banker 's discount = ₹1
So, the banker pays ₹(100 - 1) = ₹99.
Amount = ₹ 99
So, the bill-holder loses ₹1.
So, for investment ₹1 should be interest on ₹99 for 4 months.
 ∴ Rate of interest = Banker 's discount × 100 % Amount × Time

 ∴ Rate of interest = 1 × 100 = 100 = 3 1 % 99 × 4/12 33 33

##### Correct Option: C

 Here , 4 months = 1 years 3
 & there4; Banker deducts ₹3 × 1 = ₹1 from a bill of ₹100 3

Banker 's discount = ₹1
So, the banker pays ₹(100 - 1) = ₹99.
Amount = ₹ 99
So, the bill-holder loses ₹1.
So, for investment ₹1 should be interest on ₹99 for 4 months.
 ∴ Rate of interest = Banker 's discount × 100 % Amount × Time

 ∴ Rate of interest = 1 × 100 = 100 = 3 1 % 99 × 4/12 33 33

1. A man bought a motor-cycle for ₹32500. He sold it for ₹35000, allowing the buyer for a 6 months credit. If the money be worth 4 % per annum, the gain percent is :
1.  8 1 % 7
2.  7 9 % 13
3.  7 5 % 13
4.  8 2 % 5
5. None of these

1. Here , Selling Price of motor- cycle = ₹35000
Cost Price of motor- cycle = ₹32500
∴ Gain = Selling Price - Cost Price
Gain = ₹35000 - ₹32500
Gain = ₹2500

 ∴ Gain % = Gain × 100 % Cost Price

##### Correct Option: B

Here , Selling Price of motor- cycle = ₹35000
Cost Price of motor- cycle = ₹32500
∴ Gain = Selling Price - Cost Price
Gain = ₹35000 - ₹32500
Gain = ₹2500

 ∴ Gain % = Gain × 100 % Cost Price

 ∴ Gain % = 2500 × 100 % 32500
 = 100 % = 7 9 % 13 7

1. At a given rate, the simple interest and the true discount on a certain sum, for a given time, are ₹24 and ₹22, respectively. The sum is :
1. ₹264
2. ₹220
3. ₹288
4. ₹295
5. None of these

1. Given :- True discount = ₹ 24 and Simple Interest = ₹ 22

 ∴ Sum Due = True discount × Simple Interest Simple Interest - True discount

##### Correct Option: A

Given :- True discount = ₹ 24 and Simple Interest = ₹ 22

 ∴ Sum Due = True discount × Simple Interest = 24 × 22 = ₹ 264 Simple Interest - True discount 24 - 22

1. The holder of a bill for ₹17850 nominally due on May 21, 1991 received ₹357 less than the amount of the bill by having it discounted at 5 %. When was it discounted?
1. Dec 29, 1990
2. Dec 30, 1989
3. Dec 19, 1990
4. Dec 20, 1995
5. None of these

1. Here , Amount = ₹17850 , Rate = 5% ,
S.I. on ₹17850 at 5% is ₹357.

 ∴ Time = S.I. x 100 Amount x Rate

 Time = 100 × 357 = 2 Year = 146 Days 17850 × 5 5

So, the bill is 146 days prior to May 24, the legally due date.
Sum of the number of Days ( May + April + March + Feb. + Jan. + Dec. ) = 24 + 30 + 31 + 28 + 31 + 2 = 146 days So, the bill was discounted on Dec 29, 1990.

##### Correct Option: A

Here , Amount = ₹17850 , Rate = 5% ,
S.I. on ₹17850 at 5% is ₹357.

 ∴ Time = S.I. x 100 Amount x Rate

 Time = 100 × 357 = 2 Year = 146 Days 17850 × 5 5

So, the bill is 146 days prior to May 24, the legally due date.
Sum of the number of Days ( May + April + March + Feb. + Jan. + Dec. ) = 24 + 30 + 31 + 28 + 31 + 2 = 146 days So, the bill was discounted on Dec 29, 1990.