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Examples 4 to 6

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(4) A certain sum amounts to Rs. 5800 in 2 years, Rs. 7400 in 6 years.  Find the rate and the sum.

Soln. Here,

P  +  6I   =  7400
  ( Amount for 6 yrs. )

P  +  2I   =  5800
( Amount for 2 yrs. )
\therefore  4I =   1600

\therefore  I  =  Rs.  400       ( p.a. ) P  = A  –  2 I  =  5800 – 800 = Rs. 5000

i.e.  for N  = 1,  I  =  400  &  P  =  5000

Now,   I   =  \frac{PRN}{100}

\therefore 400   =    \frac{5000\times R \times1}{100}

\therefore  R   =    8   %

(5) At what rate per cent per annum will a sum of  money double in  10  years ?

Soln. Here,  N  =  10,  x  =  2

Now,   N   =   \frac{100\left (x-1 \right )}{R}

\therefore  R   =   \frac{100\left (x-1 \right )}{N}   =   \frac{100\left (2-1 \right )}{10}   =  10   %

(6) A sum was put at simple interest at a certain rate for 3 years.  Had it been put at  5 %  higher rate, it would have fetched  Rs. 7500 more. Find the sum.

Soln. Difference  in   I    =   \frac{P\times\left ( \textup{Diffrence in R} \right ) \times N}{100}

\therefore  7500   =    \frac{\textup{p }\times5 \times3}{100}     \therefore P   =   Rs.  50000

OR

5  %   =  Rs.  7500             ( For  5  years )

\therefore 5  %   =  Rs.  2500      ( For  1  year)

\therefore 100  %   =  Rs.  50000

i.e.  P  =   Rs.  50000    ( Principal is always taken as 100  % )

 

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