A) Sum = Rs.400 and Time = 5 years | B) Sum = Rs.200 and Time = 2.5 years |

C) Sum = Rs.400 and Time = 2.5 years | D) Sum = Rs.200 and Time = 5 years |

Explanation:

BD = Rs.100

TD = Rs.80

R = 10%

$F=\frac{BD\times TD}{BD-TD}=\frac{100\times 80}{100-80}=Rs.400$

BD = Simple interest on the face value of the bill for unexpired time= FTR/100

$\Rightarrow 100=\frac{400\times T\times 10}{100}\phantom{\rule{0ex}{0ex}}$

=> T = 2.5 years

A) 8 months | B) 11 months |

C) 10 months | D) 9 months |

Explanation:

F = Rs. 498

TD = Rs. 18

PW = F - TD = 498 - 18 = Rs. 480

R = 5%

$TD=\frac{PW\times TR}{100}$

$\Rightarrow 18=\frac{480\times T\times 5}{100}$

=> T = 3/4 years = 9 months

A) Rs. 2 | B) Rs. 1.25 |

C) Rs. 2.25 | D) Rs. 0.5 |

Explanation:

F = Rs. 8100

R = 5%

T = 3 months = 1/4 years

$BD=\frac{FTR}{100}=\frac{8100\times {\displaystyle \frac{1}{4}}\times 5}{100}=Rs.101.25$

$TD=\frac{FTR}{100+TR}=\frac{8100\times {\displaystyle \frac{1}{4}}\times 5}{100+\left({\displaystyle \frac{1}{4}}\times 5\right)}=Rs.100$

Therefore BD - TD = 101.25-100 = Rs.1.25

A) Rs. 24 | B) Rs. 12 |

C) Rs. 36 | D) Rs. 18 |

Explanation:

T= 6 months = 1/2 year

R = 6%

$TD=\frac{BD\times 100}{100+TR}=\frac{18.54\times 100}{100+\left({\displaystyle \frac{1}{2}}\times 6\right)}=Rs.18$

A) Rs. 400 | B) Rs. 300 |

C) Rs. 100 | D) Rs. 200 |

Explanation:

$F=\frac{BD\times TD}{BD-TD}=\frac{200\times 100}{200-100}=\frac{200\times 100}{100}=Rs.200$

A) Rs. 4500 | B) Rs. 6000 |

C) Rs. 5000 | D) Rs. 4000 |

Explanation:

T = 4 years

R = 5%

Banker's Gain, BG = Rs.200

$TD=\frac{BG\times 100}{TR}=\frac{200\times 100}{4\times 5}=Rs.1000$

$TD=\sqrt{PW\times BG}$

$\Rightarrow 1000=\sqrt{PW\times 200}$

=>PW = Rs.5000

A) Rs. 1600 | B) Rs. 1200 |

C) Rs. 1800 | D) Rs. 1400 |

Explanation:

Since the compound interest is taken here,

$PW{\left(1+\frac{5}{100}\right)}^{2}=1764$

=> PW = 1600

A) Rs. 432 | B) Rs. 422 |

C) Rs. 412 | D) Rs. 442 |

Explanation:

F = Rs. 2160

TD = Rs. 360

PW = F - TD = 2160 - 360 = Rs. 1800

True Discount is the Simple Interest on the present value for unexpired time

=>Simple Interest on Rs. 1800 for unexpired time = Rs. 360

Banker's Discount is the Simple Interest on the face value of the bill for unexpired time

= Simple Interest on Rs. 2160 for unexpired time

=(360/1800)* 2160

= (1/5) * 2160

=Rs. 432

A) Rs. 21 | B) Rs. 17 |

C) Rs. 18 | D) Rs. 34 |

Explanation:

$BG=\frac{{\left(TD\right)}^{2}}{PW}=\frac{(340{)}^{2}}{3400}=Rs.34$