# True Discount

## True Discount

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Question 1 |

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

A | Rs. 20 |

B | Rs. 21.81 |

C | Rs. 22 |

D | Rs. 18.33 |

Question 1 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.(20/120) x 110 = Rs. 18.33

Question 2 |

The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is:

A | Rs. 1386 |

B | Rs. 1764 |

C | Rs. 1575 |

D | Rs. 2268 |

Question 2 Explanation:

Let P.W. be Rs. y.
Then, S.I. on Rs. y at 16% for 9 months = Rs. 189.
y x 16 x(9/12) x(1/100)= 189 or y = 1575.
P.W. = Rs. 1575.
Sum due = P.W. + T.D. = Rs. (1575 + 189) = Rs. 1764.

Question 3 |

A man buys a watch for Rs. 1950 in cash and sells it for Rs. 2200 at a credit of 1 year. If the rate of interest is 10% per annum, the man:

A | gains Rs. 55 |

B | gains Rs. 50 |

C | loses Rs. 30 |

D | gains Rs. 30 |

Question 3 Explanation:

S.P.= P.W. of Rs. 2200 due 1 year hence = Rs.((2200 x 100)/100 + (10 x 1))= Rs. 2000.
Gain = Rs. (2000 - 1950) = Rs. 50.

Question 4 |

The true discount on Rs. 1760 due after a certain time at 12% per annum is Rs. 160. The time after which it is due is:

A | 6 months |

B | 8 months |

C | 9 months |

D | 10 months |

Question 4 Explanation:

P.W. = Rs. (1760 -160) = Rs. 1600.
S.I. on Rs. 1600 at 12% is Rs. 160.
Time = (100 x 160)/(1600 x 12)) ==> 5/6years ==>(5/6)x 12months = 10 months.

Question 5 |

The present worth of Rs. 2310 due 5/2 years hence, the rate of interest being 15% per annum, is:

A | Rs. 1750 |

B | Rs. 1680 |

C | Rs. 1840 |

D | Rs. 1443.75 |

Question 5 Explanation:

P.W. = Rs.((100 x 2310)/(100+(15*(5/2))) ==> Rs. 1680

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