**True Discount** Aptitude Question and Answer – Formulas & Tricks

**Present Value(PW):** The Present value or present worth of a sum of money due at the end of a given time at the given rate will amount to the due.

**True Discount(TD):** The True Discount is the difference between the sum due at the end of a given time and its present worth.

Thus, True Discount = Amount – Present Worth

**Note:**

- Clearly True Discount in the interest on the present worth(PW) and Amount (A) = Present Worth (PW) + True Discount (TD)
- Interest is reckoned on the Present Worth (PW) and the True Discount (TD) is reckoned on amount.

Let rate = R% per annum and Time = T years. Then,

- PW = (100 * Amount) / (100 + (R + T)) = (100 * TD) / (R * T)
- TD = (PW * R * T ) / 100 = (Amount * R * T) / (100 + (R * T))
- Amount = PW + TD
- Interest is reckoned on RW and true discount is reckoned on the amount.
- Sum =(SI * TD) / (SI – TD)
- SI – TD = SI on TD
- When the sum is put at compound interest, then PW = Amount / (1 + (R / 100))
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**True Discount Aptitude Question and Answer With Detailed Explanation** – Quantitative Aptitude

## True Discount

Question 1 |

A trade owes a merchant Rs. 10, 028 due 1 year hence. The trader wants to settle the account after 3 months. If the rate of interest 2%per annum, how much cash should he pay?

Rs. 9025 | |

Rs. 9200 | |

Rs. 9600 | |

Rs. 9800 |

Question 1 Explanation:

**Answer: Option B**

__Explanation:__

Required Money = P.W of Rs. 10028 due 9 months hence

**Cash should he pay = Rs. 9200**

Question 2 |

If Rs. 10 be allowed as true discount on a bill of Rs. 110 due at the end of a certain time, then the discount allowed on the same sum due at the end of double the time is:

Rs. 20 | |

Rs. 21.81 | |

Rs. 22 | |

Rs. 18.33 |

Question 2 Explanation:

**Answer: Option D**

__Explanation:__

S.I. on Rs. (110-10) for a certain time = Rs.10

S.I. on Rs. 100 for double the time = Rs. 20

T.D on Rs. 120 = Rs(120-100) = Rs.20

T.D on Rs 110 = Rs((20/120) *110) = Rs. 18.33

Question 3 |

The interest on Rs.750 for 2 years is the same as the true discount on Rs. 960 due 2 years hence. If the ratio of interest is the same in both cases, it is:

12% | |

14% | |

15% | |

16% |

Question 3 Explanation:

**Answer: Option B**

__Explanation:__

S.I on Rs. 750 = T.D on Rs. 960

This means P.W of Rs. 960 due 2 years hence is Rs. 750

Therefore, T.D = Rs (960-750) = Rs. 210

Thus, S.I on Rs. 750 for 2 years is Rs. 210.

Question 4 |

The Simple interest and the true discount on a certain sum for a given time and at a given rate are Rs. 85 and Rs.80 respectively. The sum is:

Rs. 1800 | |

Rs. 1450 | |

Rs. 1360 | |

Rs. 6800 |

Question 4 Explanation:

**Answer: Option C**

__Explanation:__

**Sum = Rs. 1360**

Question 5 |

If the true discount on sum due 2 years hence at 14% per annum be Rs. 168, the sum due is:

Rs. 768 | |

Rs. 968 | |

Rs. 1960 | |

Rs. 2400 |

Question 5 Explanation:

**Answer: Option A**

__Explanation:__

P.W = 600

Therefore, Sum = (PW + TD)

=Rs.(600 + 168)

**Sum= Rs. 768**

Question 6 |

The profit earned by selling an article for Rs. 900 is double the loss incurred when the same article is sold for Rs. 490. At what price should the artical be sold to make 25% profit?

715 | |

469 | |

400 | |

750 |

Question 6 Explanation:

**Answer: Option D**

__Explanation:__

Let CP be Rs. x

900 - x = 2 * ( x - 450 ) That, is x = Rs. 600

C.P = 600 gain required is 25%

S.P = [( 100 + 25 ) * 600] / 100

**S.P = Rs. 750**

Question 7 |

A man buys a watch for Rs. 1950 in cash and sell it for Rs.2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:

Gain Rs. 60 | |

Gain Rs. 50 | |

Gain Rs. 70 | |

Gain Rs. 100 |

Question 7 Explanation:

**Answer: Option B**

__Explanation:__

S.P = PW of Rs. 2200 due 1 year

= Rs. 2200 * 100 / 100 + (10 * 1)

=Rs. 2000

Gain = Rs. (2000 - 1950)

**Gain = Rs. 50**

Question 8 |

A man purchased a cow for Rs. 3000 and sold it the same day for Rs. 3600, allowing the buyer a credit of 2 years. If the rate of interest be 10% per annum, then the man has a gain of:

0% | |

5% | |

7.5% | |

10% |

Question 8 Explanation:

**Answer: Option A**

__Explanation:__

CP = Rs. 3000

SP = Rs. [3600 * 10] / [100 + (10 * 2)] = Rs. 3000

**Gain = 0%**

Question 9 |

Find the present worth of Rs. 930 due 3 Years hence at 8% per annum. Also find the discount?

186 | |

180 | |

185 | |

189 |

Question 9 Explanation:

**Answer: Option B**

__Explanation:__

PW = [100 * Amount] / [100 + (R * T)]

=[100 * 930] / [100 + (8 * 3)] = Rs. 750

TD = Amount -PW

**TD = 930 - 750 =Rs. 180**

Question 10 |

If the true discount on sum due 2 years hence at 14% per annum be Rs. 168, the sum due is

Rs. 600 | |

Rs. 768 | |

Rs. 878 | |

Rs. 668 |

Question 10 Explanation:

**Answer: Option B**

__Explanation:__

We know that,

PW = 100 * TD / R * T

=100 * 168 / 14 * 2

PW = 600

Now , Required Sum = (PW + TD)

=Rs (600 + 168)

**Sum = Rs. 768**

There are 10 questions to complete.