# True Discount Questions

**FACTS AND FORMULAE FOR TRUE DISCOUNT QUESTIONS**

Suppose a man has to pay Rs.156 after 4 years and the rate of interest is 14% per annum. Clearly, Rs. 100 at 14% will amount to Rs. 156 in 4 years. So, the payment of Rs. 100 now will clear off the debt of Rs.156 due 4 years. Hence, we say that :

Sum due = Rs.156 due 4 years hence;

Present Worth (P.W) = Rs. 100;

True Discount (T.D) = (Sum due) - (P.W)=Rs. (156 - 100) = Rs. 56

We define :

** T.D = Interest on P.W**

** Amount = (P.W) + (T.D)**

Interest is reckoned on P.W and true discount is reckoned on the amount.

**IMPORTANT FORMULAE**

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

**1.**

**2.**

**3.**

**4.** (S.I) - (T.D )= S.I on T.D

**5.** When the sum is put at compound interest, then

A) 715 | B) 469 |

C) 400 | D) 750 |

Explanation:

Let C.P be Rs. x

900 - x = 2(x - 450)

=> x = Rs.600

C.P = 600 gain required is 25%

S.P = [(100+25)*600]/100

= Rs.750

A) gains Rs. 55 | B) gains Rs. 50 |

C) loses Rs. 30 | D) gains Rs. 30 |

A) Rs.6800 | B) Rs.6500 |

C) Rs.6000 | D) Rs.6200 |

A) Rs.12880 | B) Rs.12000 |

C) Both are equally good | D) None of the above |

Explanation:

PW of Rs.12,880 due 8 months hence

= Rs[(12880 x 100)/(100+(18 x 8/12))] =Rs.11500

Clearly 12000 in cash is a better offer.

A) 0% | B) 5% |

C) 7.5% | D) 10% |

Explanation:

C.P =Rs.3000

S.P =Rs. [3600*10]/[100+(10*2)] = Rs.3000

Gain =0%

A) 12% | B) 13% |

C) 15% | D) 14% |

Explanation:

P.W = 2562-122 =Rs.2440

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

A) 1320 | B) 1300 |

C) 1325 | D) 1200 |

Explanation:

Required Sum = PW of Rs.702 due 6 months hence + PW of Rs.702 due 1 year hence

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

=Rs.1325

A) 186 | B) 180 |

C) 185 | D) 189 |

Explanation:

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

=[(100 x 930)/(100+(8x3))] = Rs. 750

T.D = Amount - P.W = 930 - 750 = Rs.180