पृष्ठम्:Ganita Sara Sangraha - Sanskrit.djvu/३०७

CHAPTER VIMIXED PROBLEMS gave in discharge of the debt the sum of a series m arithmetical progression consisting of terms and gave also the interest, accruing on those multiples of S The deht amount (corresponding to the sum of the series), the interest (which he paid), and the time of discharge (of that debt)-tell me, friend, after calculating. what the (respective) value of these quantities is The rule for arriving at the average common interest - 77 and 77. Divide the sum of the (various accruing) interests by the sun of the (various corresponding) interests due for a month; the resulting quotient is the required time. The product of the (assumed) rate-time and the rate-capital is divided by this required time, then multiplied by the sum of the (various accruing) interests and then divided again by the sum of the various given) capital amounts. This gives rise to the (required) rate-interest In example in illustration thereaf 78. In this problem, four hundreds were (separately) invested at the (respective) rates of 2, 3, 5 and 4 per cent (per menscm) for 5, 4, 2 and 3 months (respectively) What is the average common time of investment, and what the average common rate of interest? Thus end the problems hearing on interest in this chapter on mixed problems. 77 and 773 The various accrumg interests are the various amounts of uterests accruing on the several amounts at the varions 1ates for their respective penods. Symbolically, [c₁ x 4₁ x 1₁ Tx C 109 CX t x 1₂ Tx C C₂ x1 x Ig Tx C + ₁x1x1₁. +.. and 2x0x [x 1₁ x 1₁ C₂ x to x I: +.. + ta Tx C 7x C ·}=t .} ÷ (0₁ + 0₂ + = 01 avelage interest. + tu 01 average time;