# Problems on Banker's Discount

Q1. The present worth of a sum due sometime hence is Rs. 1600 and the true discount is Rs. 160. The banker's gain is

(a) Rs. 16

(b) Rs. 21

(c) Rs. 24

(d) Rs. 29

**Answer:** (a) Rs. 16

S.I on Rs. 1600 = Rs. 160

S.I on Rs. 1760 = Rs. (160/1600) X 1760 = Rs. 176

∴ True discount = Rs. 160

Banker's discount = Rs. 176

∴ Banker's gain = Rs. 176 - Rs. 160 = Rs. 16

Q2. The banker's gain of a sum due 4 years hence at 5% per annum is Rs. 25. The present worth is

(a) Rs. 595

(b) Rs. 610

(c) Rs. 625

(d) Rs. 640

**Answer:** (c) Rs. 625

True discount (T.D) = | B.G X 100 | = Rs. | 25 X 100 | = Rs. 125 |

R X T | 5 X 4 |

Present worth = | 100 X T.D | = | 100 X 125 | = Rs. 625 |

R X T | 5 X 4 |

Q3. The banker's gain on a sum due 4 years hence at 5% per annum is Rs. 250. The banker's discount is

(a) Rs. 1175

(b) Rs. 1200

(c) Rs. 1350

(d) Rs. 1500

**Answer:** (d) Rs. 1500

True discount (T.D) = | Banker's gain X 100 | = Rs. | 250 X 100 | = Rs. 1250 |

R X T | 5 X 4 |

∴ B.D = Rs. 1250 + 250 = Rs. 1500

Q4. The banker's discount on a certain sum due 2 years hence is ^{11}/_{10} of the true discount. The rate percent per annum is

(a) 5%

(b) 6%

(c) 8%

(d) 9%

**Answer:** (a) 5%

Let T.D be Rs. x

∴ B.D = Rs. ^{11x}/_{10}

Sum = | B.D X T.D | = | ^{11x}/_{10} X x |
= | ^{11x2}/_{10} |
= 11x |

B.D - T.D | ^{11x}/_{10} - x |
^{x}/_{10} |

S.I on Rs. 11x for 2 years is Rs. ^{11x}/_{10}

∴ Rate = ( | 100 X ^{11x}/_{10} |
) = 5% |

11x X 2 |

Q5. The banker's discount on Rs. 1500 at 10% per annum is the same as the true discount of Rs. 1550 for the same time and at the same rate. The time is

(a) ^{15}/_{4} months

(b) ^{15}/_{4} months

(c) ^{15}/_{4} months

(d) ^{15}/_{4} months

**Answer:** (c) ^{15}/_{4} months

Present Worth of Rs. 1550 is Rs. 1500

S.I = Rs. 1550 - 1500 = Rs. 50

∴ Time = | 100 X 50 | years = | 5 | years = | 5 X 12 | months = | 15 | months |

1600 X 10 | 16 | 16 | 4 |

Q6. The true discount on bill of Rs. 640 is Rs. 80. The banker's discount is

(a) Rs. 91.42

(b) Rs. 94.49

(c) Rs. 97.52

(d) Rs. 102.65

**Answer:** (a) Rs. 91.42

Present Worth = Rs. (640 - 80) = Rs. 560

S.I on Rs. 560 = Rs. 80

S.I on Rs. 640 = Rs. (80/560) X 640 = Rs. 91.42

∴ B.D = Rs. 91.42

Q7. The present worth of a bill due sometime hence is Rs. 1200 and the True discount on the bill is Rs. 120. Find B.D and B.G is

(a) Rs. 112

(b) Rs. 121

(c) Rs. 127

(d) Rs. 132

**Answer:** (b) Rs. 121

B.G = | (TD)^{2} |
= Rs. | 120 X 120 | = Rs. 12 |

PW | 1200 |

B.D = (T.D + B.G) = Rs. (110 + 11) = Rs. 121

Q8. The present worth of a sum due sometime hence is Rs. 625 and the banker's gain is Rs. 25. The true discount is

(a) Rs. 111

(b) Rs. 119

(c) Rs. 125

(d) Rs. 133

**Answer:** (c) Rs. 125

T.D = √P.W X B.G = √625 X 25 = Rs. 25 X 5 = Rs. 125

Q9. The B.D and T.D on a sum due 8 months hence are Rs. 110 and Rs. 100 respectively. Find the sum and the rate percent.

(a) 11%

(b) 15%

(c) 19%

(d) 21%

**Answer:** (b) 15%

Sum = | B.D X T.D | = Rs. | 110 X 100 | = Rs. 1100 |

B.D - T.D | 110 - 100 |

Now B.D = S.I on sum due

∴ S.I on Rs. 1100 for 8 months is Rs. 110

Rate = | 100 X 110 | = | 110 X 12 | = 15% |

1100 X (8/12) | 11 X 8 |

Q10. The banker's discount on a sum of money is Rs. 72 and the true discount on the same sum for the same time is Rs. 60. The sum due is

(a) Rs. 260

(b) Rs. 285

(c) Rs. 330

(d) Rs. 360

**Answer:** (d) Rs. 360

Sum = | B.D X T.D | = Rs. | 72 X 60 | = Rs. | 72 X 60 | = Rs. 360 |

B.D - T.D | 72 - 60 | 12 |

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