# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२९९

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CHAPTER VI-MIXED PROBLEMS.

interest) is divided by the difference between those periods, what happens to be the quotient is the required capital in relation to (all) those (given mixed sums).

Examples in illustration thereof

43. The mixed sums are 50, 58 and 66, and the months (during which interest has accrued respectively) are 5, 7 and 9. Find out what the interest is (in each case)

49 and 50. O arithmetician, a certain man paid out to 4 persons 30, ${\displaystyle 31{\tfrac {2}{3}}}$, ${\displaystyle 33{\tfrac {1}{3}}}$ and 35, (these) being the mixed sums (of the same capital and the interest due thereon) at the end of 3, 4, 5 and 6 months (respectively). Tell me quickly, what may be the capital here ?

The rule for separating the capital, which is of the same value in all cases, and the time (during which interest has accrued}, from their mixed sum :-

51. Wise men say that that is the (required) capital, which is obtained as the quotient of the difference between (any two of) the (given ) mixed sums as multiplied by each other's interest, when this (difference) is divided by the difference between the (two chosen) amounts of interest.

Examples in illustration thereof.

52. The (given) mixed sums of the capital and the periods of interest are 21, 23 and 25; here, (in this problem,) the amounts of interest are 6, 10 and 14. What may be the capital of equal value here ?

53. The (given) mixed suns are 35, 37 and 39; and the amounts of interest are 20, 28 and 36. (What is the common capital ?)

51.^ Symbolically, ${\displaystyle {\tfrac {m_{1}i_{2}\backsim m_{2}i_{1}}{i_{1}\backsim i_{2}}}=c}$, where ${\displaystyle m_{1},m_{2},}$etc., are the various miśras or mixed sums.