# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३०१

एतत् पृष्ठम् परिष्कृतम् अस्ति
105
CHAPTER VI-MIXED PROBLEMS.

3. The monthly interest on 60 is exactly 5. The capital lent out is 35; the (amount of the) installment (to be paid) is 15 in (every) 3 months. What is the time (of discharge) of that (debt) ?

The rule for separating various capital amounts, on which the sume interest has accrued, from their mixed sum:-

. Let the (given) nixed sum multiplied by the time (give) in relation to it be divided by the sum of that quantity, wherein are combined the various rate-capitals as multiplied by their respective rate-times and as divided by their respective rate-interests. Ihe interest (is thus arrived at); and (from this) the capital amounts are arrived at as before.

Examples in illustration thereof.

61. The mixed sum (of the capital amounts lent out) at the rates of 2, 6 and 4 per cent per mensem is 4,400. Here the capital amounts are such as have equal amounts of interest accruing after 2 months. What (and the capital amounts lent, and what is the equal interest)?

62. An amount represented (on the whole) by 1,900 was lent out at the rates of 3 per cent, 5 per 70, and $3{\tfrac {1}{2}}$ per 60 (per mensem); the interest (accrued) in 3 months (on the various lent parts of this capital amount) is the same (in each case). (What are these amounts lent out and what is the interest?)

The rule for arriving at the lent out capital in relation to the known time of discharge by instalments:-

. Lat the amount of the installment as divided by the time thereof and as multiplied by the time of discharge be divided by

60.^ Symbolically, ${\tfrac {m\times t}{{\tfrac {C_{1}\times T_{1}}{I_{1}}}+{\tfrac {C_{2}\times T_{2}}{I_{2}}}+\&c}}=i$ , from this, the capitals are found out by the rule in Ch. VI.10.

63.^ Symbolically, ${\tfrac {{\tfrac {s}{p}}t}{1+{\tfrac {1\times t\times I}{T\times C}}}}=c$ , where s=amount of installment, p=the time of an installment, and t=the time of discharge. 