text: # पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३००
  
  एतत् पृष्ठम् परिष्कृतम् अस्ति
  104
  GAŅIITASĀRASAŃGRAHA.
  
  The rule for arriving at the capital dealt out at two different rates of interest:-
  
  54.[54] Let the balance quantity (i.e., the difference between the two amounts of interest,) be divided by the difference between those (two quantities) which form the interest on one for the given periods of time; (this quotient) becomes the capital thought of by one's self before.
  
  Examples in illustration thereof.
  
  55. Borrowing at the rate of 6 percent, and then lending out at the rate of 9 per cent, one obtains in the way of the differential gain 81 duly at the end of 3 months. What is the capital (utilized here) ?
  
  56. Borrowed at the rate of 3 per cent per mensem, a certain capital amount is put out to interest at the rate of 8 per cent per mensem. The differential gain is 80 at the end of 2 months. How much is the capital (so used)?
  
  The rule for arriving at the time when both capital and interest will become paid up (by installments):-
  
  57.[57] The capital lent out is multiplied by its time (of installment) and is again multiplied by the rate-interest; this product, when divided by the rate-capital and the rate-time, becomes the interest in relation to the installment. The capital (in the installment) and the time (of discharge of the debt are to be made out) as before from (this) interest.
  
  Examples in illustration thereof.
  
  58. The rate of interest is 5 for 70 per mensem; the (amount of the) installment to be paid is 18 in (every) 2 months; the capital lent out is 84. What is the time of discharge?
  
  54.^  Symbolically, ${\displaystyle {\tfrac {i_{1}\backsim i_{2}}{{\tfrac {1\times t_{1}\times I_{1}}{T_{1}\times C_{1}}}-{\tfrac {1\times t_{2}\times I_{2}}{T_{2}\times C_{2}}}}}=c}$.
  
  57.^ Symbolically, ${\displaystyle {\tfrac {c\times p\times I}{C\times T}}=}$ interest in the installment, where p is the time of each installment.
explanation: The document is a section from a mathematical text, "Ganitasarasangraha," which deals with financial mathematics, specifically rules and examples related to interest calculations and capital. It contains several questions and their corresponding answers, including problems related to calculating capital based on differential interest rates and determining the time required to pay off a debt with installments.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
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distilabel_metadata.role: system
distilabel_metadata.content: # पृष्ठम्:गणितसारसङ्ग्रहः॒रङ्गाचार्येणानूदितः॒१९१२.djvu/३००
  
  एतत् पृष्ठम् परिष्कृतम् अस्ति
  104
  GAŅIITASĀRASAŃGRAHA.
  
  The rule for arriving at the capital dealt out at two different rates of interest:-
  
  54.[54] Let the balance quantity (i.e., the difference between the two amounts of interest,) be divided by the difference between those (two quantities) which form the interest on one for the given periods of time; (this quotient) becomes the capital thought of by one's self before.
  
  Examples in illustration thereof.
  
  55. Borrowing at the rate of 6 percent, and then lending out at the rate of 9 per cent, one obtains in the way of the differential gain 81 duly at the end of 3 months. What is the capital (utilized here) ?
  
  56. Borrowed at the rate of 3 per cent per mensem, a certain capital amount is put out to interest at the rate of 8 per cent per mensem. The differential gain is 80 at the end of 2 months. How much is the capital (so used)?
  
  The rule for arriving at the time when both capital and interest will become paid up (by installments):-
  
  57.[57] The capital lent out is multiplied by its time (of installment) and is again multiplied by the rate-interest; this product, when divided by the rate-capital and the rate-time, becomes the interest in relation to the installment. The capital (in the installment) and the time (of discharge of the debt are to be made out) as before from (this) interest.
  
  Examples in illustration thereof.
  
  58. The rate of interest is 5 for 70 per mensem; the (amount of the) installment to be paid is 18 in (every) 2 months; the capital lent out is 84. What is the time of discharge?
  
  54.^  Symbolically, ${\displaystyle {\tfrac {i_{1}\backsim i_{2}}{{\tfrac {1\times t_{1}\times I_{1}}{T_{1}\times C_{1}}}-{\tfrac {1\times t_{2}\times I_{2}}{T_{2}\times C_{2}}}}}=c}$.
  
  57.^ Symbolically, ${\displaystyle {\tfrac {c\times p\times I}{C\times T}}=}$ interest in the installment, where p is the time of each installment.
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document is a section from a mathematical text, "Ganitasarasangraha," which deals with financial mathematics, specifically rules and examples related to interest calculations and capital. It contains several questions and their corresponding answers, including problems related to calculating capital based on differential interest rates and determining the time required to pay off a debt with installments.
  
  Label: multiple-question-and-answer