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CHAPTER VI-MIXED PROBLEMS.
90
60 is (the value of) the time combined with the capital lont 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-timo, by the given interest and by four, and is thon 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 80 as to carry out the process of swikramana.
An rcample in illustration thereof. 34. The mixed sum of tho rate-interest and of the timo (for which interest has acerned) at the rate of the quantity to be found out per 100 per month and a half is 12, the capital lont out being 30 and the interest accrming thereon beliny 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 tho interest from their mixeil eum :
35. Any (optionally chosen) quantity subtracted from the given mixed eum may happen to be the time reunired. By mennis of the interest on one for that same time, to which interest one is a ldod, (the quantity remaining after the optionally chosen time is subtractal, from the given mixed suni) is to be divided. (The resulting quotient) is the required capital. Tho mixod 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 per cont (per monsem), the quantities representing the time, the capital and the interest
33. Symbolically
?...*T*1in used with m in carrying out
the required sankramara, m being equal to 1 +t,
35. Here, of the three unknown quantities, the value of the time is to be optionally chosen, and the other two quautities aro arrivod at in socordance with rule in Ch. VI. 21.
