# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२९७

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101
CHAPTER VI--MIXED PROBLEMS.

dividing the various amounts of interest by their corresponding period of time. Thus the various capital amounts happen to be found out.

Examples in illustration thereof.

49. (Sums represented by) 10, 6, 3 and 15 are the (various given) amounts of interest, and 5, 4, 3 and 6 are the (corresponding) months (for which those amounts of interest have accrued); the mixed sum of the (corresponding) capital amounts is seen to be ${\displaystyle 14{\tfrac {1}{2}}}$. (Find out these capital amounts.)

41. The (various) amounts of interest are ${\displaystyle {\tfrac {5}{2}}}$, 6, ${\displaystyle 10{\tfrac {1}{2}}}$, 16 and 30; (the corresponding periods of time are) 5, 6, 7, 8 and 10 months; 80 is the mixed sum (of the various capital amounts lent out. What are these amounts respectively ?)

The rule for arriving separately at the various periods of time from their given mixed sum:-

[42]. Let the quantity representing the mixed sum of the (various) periods of time be divided by the sum of those (various quotients) obtained by dividing the various amounts of interest by their corresponding capital amounts; and (then) let the (resulting) quotient be multiplied (separately by each of the above mentioned quotients). (Thus) the (various) periods of time happen to be found out.

An example in illustration thereof

43. Here, (in this problem, the (given) capital amounts are 40, 30, 20 and 50; and 10, 6, 3 and 15 are the (corresponding) amounts of interest; 18 is the quantity representing the mixed sum of the (respective) periods of time (for which interest has accrued. Find out those periods of time separately).

42.^ Symbolically,${\displaystyle {\tfrac {m}{{\tfrac {i_{1}}{c_{1}}}+{\tfrac {i_{2}}{c_{2}}}+{\tfrac {i_{3}}{c_{3}}}+...}}\times {\tfrac {i_{1}}{c_{1}}}=i_{1}}$ where ${\displaystyle m=t_{1}+t_{2}+t_{3}+\&c}$. Similarly ${\displaystyle t_{2},t_{3},}$ etc., may be found out