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Examples 7 to 9

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(7) A shopkeeper borrowed Rs. 30000 from money lenders. For one loan he paid  10 % and for the other  15 %  per annum. After one year, he paid Rs. 3600 as interest. How much did he borrow at each rate ?

Soln.

Thus, the ratio of  amount  at  10 %  to  15 %   =  900  :  600  =  3  : 2

\therefore Money   borrowed  at   10   %  =  Rs.\left (3000 \times \frac{3}{5} \right )   =  Rs.  18000

\therefore Money   borrowed  at   15   %  =  Rs.  30000  –  Rs.  18000  =  Rs.  12000

(8) What annual  installment   will  discharge a debt  of  Rs. 6000 due in 5 years at     10 % simple interest ?

Soln. Here,  A  =  Rs.  6000,   N  =  5  years,  R  =  10

a   =  \frac{200\textup{A}}{\textup{N}\times \left (200+\textup{RN}-\textup{R} \right )}

\therefore a    =   \frac{200 \times 6000}{5\times \left (200+50-10 \right )}    =    Rs.  1000

(9) The simple interest on a sum of money is \frac{36}{25}  of principal and the number of  yrs. equal to the rate percent per annum. The rate percent is :

Soln. Here,  I  = \frac{25}{36} \times  P,   N  =  R

Now,  I   = \frac{\textup{PRN}}{100}

\therefore \frac{36}{25}\times P   =   \frac{P \times R\times R}{100}

\therefore  \frac{36\times 100}{25}  =  \textup{R}^{2}      \therefore R   =    12   %

Best of  luck

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