Question

A certain sum amount to 5916 in 3 year and to 6960 rupees in 5 year at simple interest. Find the sum and rate percent per annum

Answer 1

The sum is Rs 227.54 and rate percent per annum is 12%.

Explanation:

Formula to find the final amount , after a principal amount P is invested at rate of interest r ( in decimal) in time t is

$A=P(1+rt)$

Given : A certain sum amount to 5916 in 3 year and to 6960 rupees in 5 year at simple interest.

i.e.  $5916=P(1+3r) ----------(1)$

$6960=P(1+5r)--------(2)$

Divide (2) by (1) , we get

$\dfrac{6960}{5916}=\dfrac{P(1+5r)}{P(1+3r)}\\\\ \dfrac{20}{17}=\dfrac{(1+5r)}{(1+3r)}\\\\ 20(1+3r)= 17(1+5r)\\\\ 20+60r=17+85r\\\\ 25r=3\\\\ r=\dfrac{3}{25}$

Put value of r in (1) , we get

$5916=P(1+3(\dfrac{25}{3}))\\\\ 5916 =P(26)\\\\ P=\dfrac{5916}{26}\approx227.54$

The value of r in percent = $\dfrac{3}{25}\times100=12\%$

Hence , the sum is Rs 227.54 and rate percent per annum is 12%.

# Learn more :

A sum of money invested at 6 percent per annum simple interest for a certain period of time yields 960 as interest . if this sum had been invested for 5 years more it would have yielded 2160 as interest . find the sum.

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