Aptitude True Discount Practice QA

44047.A man wants to sell his scooter. There are two offers, one at Rs. 12,000 cash and the other a credit of Rs. 12,880 to be paid after 8 months, money being at 18% per annum. Which is the better offer?

Rs. 12,000 in cash

Rs. 12,880 at credit

Both are equally good

none

Explanation:

P.W of Rs.12,880 due 8 months hence =Rs.$\dfrac{12,880 \times 100}{100+(18 \times \dfrac{8}{12})}$
=Rs.$\dfrac{12,880 \times 100}{112}$
=Rs.11,500

44051.Rs. 20 is the true discount on Rs. 260 due after a certain time. What will be the true discount on the same sum due after half of the former time, the rate of interest being the same?

Rs. 10

Rs. 10.40

Rs. 15.20

Rs. 13

Explanation:

S.I. on Rs. (260 - 20) for a given time = Rs. 20.
S.I. on Rs. 240 for half the time = Rs. 10.
T.D. on Rs. 250 = Rs. 10.
T.D on Rs. 260 =Rs.$[\dfrac{10}{250} \times 260 ]$=Rs.10.40

44052.A trader 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 12% per annum, how much cash should he pay?

Rs. 9025.20

Rs. 9200

Rs. 9600

Rs. 9560

Explanation:

Required money = P.W. of Rs. 10028 due 9 months hence
=Rs.$[\dfrac{10028 \times 100}{100+(12 \times \dfrac{9}{12}})]$
=Rs.9200

44053.The present worth of Rs. 1404 due in two equal half-yearly installments at 8% per annum simple interest is:

Rs. 1325

Rs. 1300

Rs. 1350

Rs. 1500

Explanation:

Required sum= P.W. of Rs. 702 due 6 months + P.W. of Rs. 702 due 1 year hence
=Rs.$[(\dfrac{100\times 702}{100+8 \times \dfrac{1}{2}}) + (\dfrac{100 \times 702}{100+(8 \times 1)})]$
= Rs. (675 + 650)
= Rs. 1325.

44054.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:

7.5%

10%

Explanation:

C.P=Rs.3000
S.P=Rs.$[\dfrac{3600 \times 100}{100+(10\times 2)}]$=Rs.3000
Gain =0%

44055.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

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.$(\dfrac{20}{120} \times 110)=Rs.18.33$

44058.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

Explanation:

sum=$\dfrac{S.I \times T.D}{(S.I)-(T.D)}$
=>$\dfrac{85 \times 80}{(85-80)}$
=Rs.1360.

44060.The present worth of Rs. 2310 due 2 years hence, the rate of interest being 15% per annum, is:

Rs. 1750

Rs. 1680

Rs. 1840

Rs. 1443.75

Explanation:

P.W=Rs.$[\dfrac{100 \times 2310 }{100+(15 \times \dfrac{5}{2})}]$=Rs.1680

44061.A merchant owes a businessman Rs 8640 due one year from Now. The merchant wants to settle the accounts after 4 months .If the rate of interest is 12% annum , find the amount he should pay.

Rs.8000

Rs.80

Rs.800

Rs.880

Explanation:

Present worth of Rs.8460 due in 8 months (after 4 months)
=$\dfrac{8640 \times 100}{100+(\dfrac{8}{12} \times 12}=\dfrac{8640}{108} \times 100$
Required sum=Rs.8000

44269.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 article be sold to make 25% profit?

715

469

400

750

Explanation:
Let C.P be Rs. x

900 - x = 2(x - 450) => x = Rs.600

C.P = 600 gain required is 25%

S.P = [(100+25) x 600] / 100 = Rs.750

44292.The true discount on a certain sum of money due 3 years hence is dollar 200 and the simple interest on the same sum for the same time and at the same rate is dollar 240. Find the sum and the rate per cent.

6.66

Explanation:

Given that,
True discount = dollar 200
Simple interest = dollar 240
Time = 3 years
Consider,
Sum due=$\dfrac{(S.I.) \times (T.D.)}{(S.I.) - (T.D.)}$
=>Sum due=$\dfrac{(240) \times (200)}{(240) - (200)}$
⇒ Sum due = dollar. 1200
Now,
Rate = $\dfrac{(100) \times (S.I.)}{(Sum due ) \times (T)}$
⇒ Rate = $\dfrac{(100) \times (240)}{(1200 ) \times (3)}$
⇒ Rate = $\dfrac{24000}{3600}$
⇒ Rate = 6.66 %
Therefore, Sum due = dollar. 1200 and Rate = 6.66 %

44293.The difference between the simple interest and true discount on a certain sum of money for 6 months at 6% per annum is Rs. 2.25 . Find the sum?

7525

2255

2575

2755

Explanation:

Given that,
Time = 6 months =$\dfrac{1}{2}$ of year
Rate =6%
Consider,
True discount = $\dfrac{A∗R∗T}{100+(R∗T)}$
=>True discount = $\dfrac{x∗6∗\dfrac{1}{2}}{100+(6∗\dfrac{1}{2})}$
=>True discount =x*$(\dfrac{6}{2})*(\dfrac{2}{206})$
=>True discount =$\dfrac{6x}{206}$
=>True discount =$\dfrac{3x}{103}$
Now,
S.I = (Amount * R * T) / 100 Simple interest =(x*6 * $\dfrac{1}{2} \times \dfrac{1}{100}$)
=> Simple interest=$\dfrac{3x}{100}$
Therefore,
$\dfrac{3x}{100}$ –$\dfrac{3x}{103}$ = 2.25
⇒ (103*3x) – (100*3x) = 2.25 * 100 * 103
⇒ x =2575
Therefore, sum due = Rs. 2575.

44294.The true discount on a bill due 10 months hence at 6% per annum is Rs. 26.25. The amount of the bill is:

Rs. 1250.25

Rs. 1150.25

Rs. 551.25

Rs. 645.25

Explanation:

Given,R=6%,T=10/12yrs,TD=Rs.26.25,A=?
TD=$\dfrac{A*R*T}{100+R*T}$
26.25=$\dfrac{A*6*\dfrac{10}{12}}{100+(6*\dfrac{10}{12})}$
26.25=$\dfrac{A*5}{105}$
A=>Rs.551.25

44299.The true discount on a bill due 9 months hence at 12 % per annum is Rs. 540. Find the amount of the bill and its present worth?

1500

1600

6200

6000

Explanation:

Given,
Rate = 12 %
Time = 9 months = $\dfrac{3}{4}$ years
Let amount be Rs.x. Then,
Consider,
True discount =$\dfrac{x \times R \times T}{100 + (R \times T)}$
⇒ 540 = $\dfrac{x∗12∗\dfrac{3}{4}}{100+(12∗\dfrac{3}{4})}$
⇒540 = $\dfrac{9x}{100+9}$
⇒ 540 = $\dfrac{9x}{109}$
⇒ 9x = 540 x 109
⇒ x = $\dfrac{540 \times 109}{9}$
x= Rs.6540
Amount = Rs. 6540.
P.W. = Rs. (6540 – 540) =Rs. 6000.

44300.What is the present value,banker's discount of Rs.104500 due in 9 months at 6% per annum?

Rs. 100000,Rs. 4702.50

Rs. 200000,Rs. 4702.50

Rs. 150000,Rs. 4702.50

Rs. 100000,Rs. 5002.50

Explanation:

Given that,
Amount = RS. 104500
Time = 9/12 years=3/4 years
Rate = 6%
Now,
Banker's Discount, BD =$\dfrac{A*T*R}{100}$
=$\dfrac{104500×3/4×6}{100}$
=1045×3/4×6
= Rs. 4702.50

Present value, PW =$\dfrac{F}{1+T(\dfrac{R}{100})}$
=$\dfrac{104500}{1+(\dfrac{3}{4})(\dfrac{6}{100})}$
=Rs. 100000

⊟ True Discount

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Aptitude True Discount Practice QA - Easy

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