# पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/२९५

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99
CHAPTER VI--MIXED PROBLEMS.

60 is (the value of) the time combined with the capital lent out, (What is the time and what the capital ? )

The rule for arriving at the separation of the rate-interest and the required time from their sum :--

33. The rate-capital is multiplied by its own rate-time, by the given interest and by four, and is then divided by the other (that is, the given) capital. The square root of the remainder (obtained by subtracting this resulting quotient) from the square of the given mixed sum is then used in relation to the mixed sum so as to carry out the process of saṅkramaṇa.

An example in illustration thereof.

34. The mixed sum of the rate-interest and of the time (for which interest has accrued) at the rate of the quantity to be found out per 100 per month and a half is ${\displaystyle 12{\tfrac {1}{2}}}$, the capital lent out being 30 and the interest accruing thereon being 5. (What is the rate of interest and what the time for which it has accrued ?)

The rule for arriving separately at the capital, time, and the interest from their mixed sum:-

35. Any (optionally chosen) quantity subtracted from the given mixed sum may happen to be the time required. By means of the interest on one for that same time, to which interest one is added, (the quantity remaining after the optionally chosen time is subtracted from the given mixed sum) is to be divided. (The resulting quotient) is the required capital. The mixed sum diminished by its own corresponding time and capital becomes the (required) interest.

An example in illustration thereof.

36. In a loan transaction at the rate of 5 percent (per mensem), the quantities representing the time, the capital and the interest

33. Symbolioally, ${\displaystyle {\sqrt {m^{2}-{\tfrac {C\times T\times i\times 4}{c}}}}}$ is used with m in carrying out the required saṅkramaṇa, m being equal to I+t.

35. Here, of the three unknown quantities, the value of the time is to be optionally chosen, and the other two quantities are arrived at in accordance with rule in Ch. VI. 21.