# True Discount Aptitude Questions and Answers – Quantitative Aptitude

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))T

True Discount Aptitude Question and Answer With Detailed ExplanationQuantitative 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?
 A Rs. 9025 B Rs. 9200 C Rs. 9600 D Rs. 9800
Question 1 Explanation:
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:
 A Rs. 20 B Rs. 21.81 C Rs. 22 D Rs. 18.33
Question 2 Explanation:
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:
 A 12% B 14% C 15% D 16%
Question 3 Explanation:
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:
 A Rs. 1800 B Rs. 1450 C Rs. 1360 D Rs. 6800
Question 4 Explanation:
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:
 A Rs. 768 B Rs. 968 C Rs. 1960 D Rs. 2400
Question 5 Explanation:
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?
 A 715 B 469 C 400 D 750
Question 6 Explanation:
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:
 A Gain Rs. 60 B Gain Rs. 50 C Gain Rs. 70 D Gain Rs. 100
Question 7 Explanation:
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:
 A 0% B 5% C 7.5% D 10%
Question 8 Explanation:
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?
 A 186 B 180 C 185 D 189
Question 9 Explanation:
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
 A Rs. 600 B Rs. 768 C Rs. 878 D Rs. 668
Question 10 Explanation: