## True Discount

#### True Discount

1. The difference between the simple interest and the true discount on a certain sum of money for 2 years at 15 % per annum at simple interest is ₹45. Find the sum.

1. Let the sum be ₹100.
Given that :- Time = 2 years
Rate = 15% per annum

 Simple Interest = ₹ 100 × 15 × 2 = ₹30 100

 True Discount = ₹ 100 × R × T 100 + (R×T)
 True Discount = ₹ 100 × 15 × 2 100 + (15×2)
 True Discount = ₹ 100 × 15 × 2 = ₹ 300 100 + (15×2) 13

The difference between Simple Interest and True Discount is
 ₹ 30 - 300 = ₹ 90 13 13
 If the difference in S.I. and True Discount is ₹ 90 ,the sum = ₹100 13

##### Correct Option: B

Let the sum be ₹100.
Given that :- Time = 2 years
Rate = 15% per annum

 Simple Interest = ₹ 100 × 15 × 2 = ₹30 100

 True Discount = ₹ 100 × R × T 100 + (R×T)
 True Discount = ₹ 100 × 15 × 2 100 + (15×2)
 True Discount = ₹ 100 × 15 × 2 = ₹ 300 100 + (15×2) 13

The difference between Simple Interest and True Discount is
 ₹ 30 - 300 = ₹ 90 13 13
 If the difference in S.I. and True Discount is ₹ 90 ,the sum = ₹100 13

If the difference in S.I. and T.D. is ₹1,
 The sum = ₹100 x 13 . 10

If the difference in S.I. and T.D. is ₹45,
 The sum = ₹100 × 13 × 45 = ₹650. 90

1. If ₹21 is the true discount on ₹371 for a certain time, what is the true discount on the same amount for double that time, the rate being the same in both the cases?

1. Here , Amount = ₹ 371 ,True discount = ₹ 21
₹21 is the interest on ₹( 371 - 21 ) = ₹350
Present worth = ₹350

 ∴ Present worth × no of year × rate = True Discount 100

 ∴ 350 × no of year × rate = 21 100
 ⇒ Number of year × rate = 2100 = 6 350

∴ Twice number of years × rate ( R x T )= 12
Now, on ₹112, the True Discount is ₹12
 ∴ on ₹371, True Discount = ₹ Amount × Rate × Time 100 + ( Rate × Time )

##### Correct Option: D

Here ,( Sum Due ) Amount = ₹ 371 , True discount = ₹ 21
₹21 is the interest on ₹( 371 - 21 ) = ₹350
Present worth = ₹350

 ∴ Present worth × no of year × rate = True Discount 100

 ∴ 350 × no of year × rate = 21 100
 ⇒ Number of year × rate = 2100 = 6 350

∴ Twice number of years × rate ( R x T )= 12
Now, on ₹112, the True Discount is ₹12
 ∴ on ₹371, True Discount = ₹ Amount × Rate × Time 100 + ( Rate × Time )

 True Discount = ₹ 12 × 371 112

True Discount = ₹39.75

1. If the simple interest on ₹2000 at 5 % p.a. is equal to the true discount on ₹2500 for the same time and at the same rate, the time is :

1. Given :- True Discount ( T.D. ) = ₹500
Rate = 5%
Present Worth ( P.W. ) = ₹2000

 ∴ Time = True Discount × 100 Year Present Worth × Rate

##### Correct Option: B

Given :- True Discount ( T.D. ) = ₹500
Rate = 5%
Present Worth ( P.W. ) = ₹2000

 ∴ Time = True Discount × 100 Year Present Worth × Rate

 Time = 500×100 = 5 Year 2000×5

1. The true discount on a certain bill due for nine months at 4 % simple interest is ₹150. Find the amount of the bill.

1. Given :- True Discount = ₹ 150 , Time = 9 months = ( 3/4 ) years

 Present worth ( P.W. ) = True Discount × 100 = ₹ 150 × 100 R × T 3/4 × 4

##### Correct Option: A

Given :- True Discount = ₹ 150 , Time = 9 months = ( 3/4 ) years

 Present worth ( P.W. ) = True Discount × 100 = ₹ 150 × 100 R × T 3/4 × 4

Present worth = 5000
∴ Amount of the bill = Present worth + True discount
Amount of the bill = ₹5000 + ₹150 = ₹5150.

1. The True Discount on a certain sum of money due in 2 years is ₹1800 and the simple interest on the same amount is ₹2232. Find the sum.

1. Given :- Simple interest = ₹ 1800 , True Discount = ₹ 2232

 Sum = Simple interest on the sum × True Discount (T.D.) Simple interest on the sum - True Discount (T.D.)
 Sum = ₹ 2232 × 1800 2232 - 2232

##### Correct Option: A

Given :- Simple interest = ₹ 1800 , True Discount = ₹ 2232

 Sum = Simple interest on the sum × True Discount (T.D.) Simple interest on the sum - True Discount (T.D.)
 Sum = ₹ 2232 × 1800 2232 - 2232
 Sum = ₹ 2232 × 1800 432

Sum = ₹9300.