Question

Sandeep borrowed rupees 3000 for 4 years and rupees 8000 Pro 2.5 years from Sonia at the same rate of interest the total interest on by Sonia is rupees 2880 find the rate of interest

Answer 1

let the rate of interest be x

then interest of Sandeep of rupees 3000 for 4 years = 3000 × x/100 ×4
= 120x

and interest of Sandeep of rupees 8000 for 2.5 years= 8000 × x/100 × 2.5
= 200x
according to the question,
interest in 3000 rupees for 4 years + interest of 8000 rupees for 2.5 years = 2880
so 120x + 200x = 2880
= 300x = 2880
= x = 2880/300
= x = 9
so the rate of interest is 9 %

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assumption

Rate of interest be p%

Situation 1st :-

Principal

= Rs. 3000

t = 4 years

$\tt{\rightarrow SI=\dfrac{P\times R\times T}{100}}$

$\tt{\rightarrow SI=\dfrac{3000\times p\times 4}{100}}$

= Rs.120p

Hence,

$\textbf{\underline{SI\;in\;1^st \;Situation}}$SI in 1st Situation :-

= Rs.120p

$\textbf{\underline{Second\;Situation}}$

Principal

= Rs. 8000

Time = 2.5 years

In mixed Fraction

$\tt{\rightarrow 2\dfrac{1}{2}}$

$\tt{\rightarrow\dfrac{5}{2}}$

Now ,

$\tt{\rightarrow SI=\dfrac{P\times R\times T}{100}}$

$\tt{\rightarrow\dfrac{8000\times p\times 5}{2\times 100}}$

= Rs. 200p

Hence,

SI in second situation

= Rs. 200p

$\textbf{\underline{Total\; interest\;by\;Sandeep}}$

= 120p + 200p

= Rs. 320p

$\textbf{\underline{Total\; interest\;gain\;by\;Sonia}}$

= Rs. 2880

Therefore

320p = 2880

$\tt{\rightarrow p=\dfrac{2880}{320}}$

p = 9 %

Hence,

Rate of interest is 9% per anum