# True Discount - Quantitative Aptitude

Q1. The present worth of Rs. 3240 due 3 years hence at 5% per annum is

(a) Rs 2500.50

(b) Rs 2817.39

(c) Rs 3215.32

(d) Rs 3389.35

**Answer:** (b) Rs 2817.39

P.W = | 100 X Amount |

100 + (R X T) |

= | 100 X 3240 |

100 + (5 X 3) |

= | 324000 |

100 + 15 |

= | 324000 |

115 |

= 2817.39

= Rs. 2817.39

Q2. The simple interest on Rs. 650 for 3 years is equal to the true discount on Rs. 720 for the same time and at the same rate. The rate of interest per annum is

(a) 3.58 %

(b) 4.28 %

(c) 4.66 %

(d) 5.32 %

**Answer:** (a) 3.58 %

S.I on Rs. 650 for 3 years = T.D on Rs. 720 for 3 years

∴ P.W of Rs. 720 for 3 years = Rs. 650

∴ T.D = Rs. 720 - 650 = Rs. 70

∴ Rate of Interest = | 100 X T.P |

P.W X T |

= | 100 X 70 |

650 X 3 |

= 3.58%

Q3. The true discount on a sum due 6 months hence at 8% per annum is Rs. 120. The sum due is

(a) Rs. 2230

(b) Rs. 2640

(c) Rs. 2958

(d) Rs. 3120

**Answer:** (d) Rs. 3120

Here T.D = Rs. 120

T = 6 months = ½ years

R = 8%

A = ?

We have P.W = | T.D X 100 |

R X T |

= | 120 X 100 |

8 X ½ |

= | 120 X 100 X 2 |

8 |

= 3000

∴ Amount = P.W + T.D = Rs. 3000 + 120 = Rs. 3120

Q4. If Rs. 20 be allowed as true discount on a bill of Rs. 220 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. 36.66

(b) Rs. 38.22

(c) Rs. 39.45

(d) Rs. 40.58

**Answer:** (a) Rs. 36.66

S.I on Rs (220 - 20) for a fix time = Rs. 20

∴ S.I on Rs. 200 for double time = Rs. 40

T.D on Rs. 240 = Rs. 40

∴ T.D on Rs. 220 = Rs. | 40 | X 220 |

240 |

= Rs. | 40 X 22 |

24 |

= Rs. 36.66

Q5. The simple interest and the true discount on a certain sum due 2 years hence are Rs. 30 and Rs. 25 respectively. The rate of interest per annum is

(a) 10%

(b) 15%

(c) 22%

(d) 28%

**Answer:** (a) 10%

Sum due = | S.I X T.D |

S.I - T.D |

= Rs. | 30 X 25 |

30 - 25 |

= Rs. | 30 X 25 |

5 |

= Rs. 150

S.I on Rs. 150 for 2 years = Rs. 30

∴ Rate = | 100 X 30 |

150 X 2 |

= 10%

Q6. If Rs.30 be allowed as true discount on a bill of Rs. 330 due after sometime, what will be the true discount on the same bill for half of the time ?

(a) Rs. 11.75

(b) Rs. 13.24

(c) Rs. 15.70

(d) Rs. 16.90

**Answer:** (c) Rs. 15.70

S.I on Rs. (330 - 30) for a fixed time = Rs. 30

∴ S.I on Rs. 300 for half time = Rs. ^{30}/_{2} = Rs. 15

∴ T.D on Rs. 315 = Rs. 15

∴ T.D on Rs. 330 = Rs. ^{15}/_{315} X 330 = Rs. 15.70

Q7. The true discount on Rs. 1250 due after a certain time at 5% per annum is Rs. 50. Find the time after which it is due

(a) 8 months

(b) 10 months

(c) 12 months

(d) 13 months

**Answer:** (b) 10 months

P.W = A - T.D = Rs. (1250 - 50) = Rs. 1200

∴ S.I = Rs. 50

P.W = Rs. 1200

R = 5%

∴ Time = | 100 X S.I |

P.W X R |

= | 100 X 50 | years |

1200 X 5 |

= | 10 | years |

12 |

= | 5 | years |

6 |

= | 5 | X 12 months |

6 |

= 10 months

Q8. The true discount on a bill due 8 months hence at 8% per annum is Rs. 200. Find the present worth of the bill.

(a) Rs. 2250

(b) Rs. 2850

(c) Rs. 3250

(d) Rs. 3750

**Answer:** (d) Rs. 3750

T = 8 months = ^{8}/_{12} years

R = 8%

T.D = Rs. 200

∴ P.W = | 100 X T.D | = | 100 X 200 | = | 100 X 200 X 12 | = Rs. 3750 |

R X T | 8 X ^{8}/_{12} |
8 X 8 |

Q9. Hari bought a radio on Rs. 1050 in cash and sold it on the same day for Rs. 1122 payable after 3 months. If the rate of interset is 8% p.a. , how much was Hari's gain ?

(a) 4.76 %

(b) 4.92 %

(c) 5.20 %

(d) 5.26 %

**Answer:** (a) 4.76 %

C.P = Rs. 1050

S.P = P.W of Rs. 1122 due 3 months hence

= Rs. | 100 X 1122 | = Rs. | 112200 | = Rs. | 112200 | = Rs. 1100 |

100 + 8 X ^{3}/_{12} |
100 + 2 | 102 |

∴ Profit = S.P - C.P = Rs (1100 - 1050) = Rs 50

∴ Gain % = ^{50}/_{1050} X 100% = 4.76%

Q10. The true discount on Rs. 3650 due after some time at 5% per annum is Rs. 150. After how much time is the sum due ?

(a) ^{3}/_{4} years

(b) ^{3}/_{5} years

(c) ^{6}/_{7} years

(d) ^{7}/_{9} years

**Answer:** (c) ^{6}/_{7} years

Here P.W = Rs. (3650 - 150) = Rs. 3500

S.I = Rs. 150

R = 5%

∴ T = | 100 X S.I | = | 100 X 150 | = | 6 | years |

P.W X R | 3500 X 5 | 7 |

**1**2