# True Discount

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2178 Directions: Each of the questions given below is followed by series of options among which you have to choose the best one. You can also review your choices by clicking into answer section.

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

A. 80

B. 750

C. 150

D. 180

Ans: Option D

Explanation:

P.W=100 x Amount /[100 + (R x T)]

=Rs.100 x 930/100+ (8×3)

= (100×930)/124 = Rs.750,

T.D. = (Amount) – (P.W.)

= Rs. (930 – 750)

= Rs. 180.

2. The true discount on a certain sum of money due 3 years hence is Rs. 250 and the simple interest on the same sum for the same time and at the same rate is Rs. 375. Find the sum and the rate percent.

A. 650, 50/3%

B. 750, 70/3%

C. 750, 50/3%

D. 650, 70/3%

Ans: Option C

Explanation:

T.D. = Rs. 250 and S.I. = Rs. 375.

Sum due =S.I. x T.D./ S.I. -T.D.

=375×250/375- 250 =Rs.750.

Rate= [100*375/750*3]%= 50/3%

3. A true discount on an amount of Rs.480 due 3 years hence is equal as simple interest on Rs.350 for 3 years at the same interest rate on true discount. Then what is the interest rate?

A. 11.34%

B. 12.38%

C. 10.92%

D. 13.12%

Ans: Option B

Explanation:

S.I on Rs.350 = T.D on Rs.480.

This means P.W of Rs.480 due 3 years hence is Rs.350.

Therefore, T.D = Rs(480 – 350) = Rs.130

Thus S.I of Rs.350 for 3 years is Rs.130.

Rate of Interest = 100 x S.I / amount x time %

= 100 x 130 / 350 x 3% = 12.38%
Hence the required rate of interest is 12.38%.

4. The true discount on Rs. 2562 due 4 months hence is Rs. 122. The rate percent is:

A.12%

B. 40/3%

C.15%

D.14%

Ans: Option C

Explanation:

P.W. = Rs. (2562 – 122) = Rs. 2440.

S.I. on Rs. 2440 for 4 months is Rs. 122.

Rate = (100 x 122)/[2440 x(1/3)]%= 15%

5. If Rs.160 and Rs.170 are true discount and simple interest of a certain amount respectively and if the time period and interest rate are equal for simple interest and true discount then the amount is:

A. Rs.2120

B. Rs.2140

C. Rs.2720

D. Rs.2180

Ans: Option C

Explanation:

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

Sum = [(S.I.) x (T.D.)]/[(S.I.) – (T.D.)]

Here, S.I = 170 and T.D = 160

Then required amount = 170 x 160 / 170 – 160

= 170 x 160/10 = 2720.

Hence the required sum is Rs.2720.

6. The difference between the simple interest and true discount on a certain sum of money for 6 months at 12% per annum is Rs.25. Find the sum.

A. 6400

B. 6800

C. 7000

D. 7200

Ans: Option B

Explanation:

Let the sum be Rs.x.

T.D. = (x*25/2*1/2)/(100+(25/2*1/2))

= x*25/4*4/425 = x/17

S.I=x*25/2*1/2*1/100=x/16

(x/16)-(x/17)=25

=>17x-16x=25*16*17

=>x=6800

Hence, sum due = Rs.6800.

7. 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?

A.Rs. 10

B.Rs. 10.40

C.Rs. 15.20

D.Rs. 13

Ans: Option B

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.(10/250)x 260= Rs. 10.40

8. A man bought a cell phone of Rs.24,000 in cash and he sold it at a credit of Rs.25760 to be paid after 8 months at 9% per annum. Then the profit/loss amount he earned is:

A. Profit of Rs.1000

B. Loss of Rs.1500

C. Loss of Rs.1000

D. Profit of Rs.1700

Ans: Option C

Explanation:

He bought cell phone at Rs.24,000 in cash.

He sold cellphone for Rs.25760 due 8 months hence at 9%.

Sum due = Rs.25760.

Note the formula, P.W. = 100 x Amount/100 + (R x T)

= 100 x T.D./R x T

Now, P.W of Rs.25760 due 8 months(8/12 year) hence

= (100 x 25760) / [100 + (18 x 8/12)]

= (25760 x 100)/112 = 23000.

Then the present worth is Rs.23000.

Hence he obtained a loss of Rs.1000.

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

A.Rs. 1325

B.Rs. 1300

C.Rs. 1350

D.Rs. 1500

Ans: Option A

Explanation:

Required sum

= P.W. of Rs. 702 due 6 months + P.W. of Rs. 702 due 1 year hence

= Rs.(100 x 702)/ 100 + 81/2+(100 x 702)/ 100 + (8 x 1)

= Rs. (675 + 650)

= Rs. 1325.

10. 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

Ans: Option C

Explanation:

Sum

= (S.I. x T.D.)/(S.I. – T.D.)=  (85 x 80)/(85 – 80)= Rs. 1360.

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

A. 6000

B. 5880

C.220

D. None of above

Ans: Option A

Explanation:

Let amount be Rs. x.

Then, x*R*T/100 + (R x T) =T.D.

=>x * 12*3/ 4/[100+[12*3/4]] =540 x

540×109 = Rs.6540

Amount = Rs. 6540.

P.W. = Rs. (6540 – 540) = Rs. 6000.

12. 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?

A.Rs. 12,000 in cash

B. 12,880 at credit

C. Both are equally good

Ans: Option A

Explanation:

P.W. of Rs.12,880 due 8 months hence

= (Rs.12880 x 100)/{100 + [18 x (8/12)]}

= (Rs.12880 x 100)/112

= Rs.11500.

13. The true discount on \$1760 due after a certain time at 12%p.a is \$160.The time after which it is due is:

A. 8 months

B. 10 months

C. 12 months

D. 15 months

Ans: Option B

Explanation:

10 months P.W=\$(1760-160) = \$ 1600

Therefore, S.I on \$1600 at 12% is \$ 160.

Therefore, Time= (100*160/1600*12)

= 5/6 yrs

=(5/6*12)months

=10 months

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