Question

if a person lends 6000 for 4 years and 8000 for 3 years at S.I the total interest earned is 2400 then the rate of interest is​

Answer 1

AnswEr :

$\bigstar\:\boxed{\sf Simple \:Interest=\dfrac{Principal \times Rate \times Time}{100}}$

• According to the Question Now :

$:\implies\sf Total \:Simple \:Interest = SI_1 + SI_2\\\\\\:\implies\sf Total \:Simple \:Interest = \dfrac{(P_1 \times R \times T_1)}{100} + \dfrac{(P_2 \times R \times T_2)}{100}\\\\\\:\implies\sf 2400= \dfrac{(60 \cancel{00} \times R \times 4)}{\cancel{100}} + \dfrac{(80\cancel{00}\times R \times 3)}{\cancel{100}}\\\\\\:\implies\sf 2400=(60 \times R \times 4) + (80 \times R \times 3)\\\\\\:\implies\sf 2400=240R +240R\\\\\\:\implies\sf 2400=480R\\\\\\:\implies\sf \cancel\dfrac{2400}{480}=R\\\\\\:\implies \boxed{\sf Rate = 5\% \:p.a.}$

⠀

∴ Rate per annum in the case will be 5%.

Answer 2

${\boxed{\sf\green{Answer: Rate\:of\:interest=5\%}}}$

_________________________

1st part:-

$\bf {Given} \begin {cases}\mathsf {P = Rs.6000}\\\mathsf{N= 4\:years}\end{cases}$

2nd part:-

$\bf{Given}\begin{cases} \sf{P = Rs.8000} \\\sf{n = 3\:years}\\\sf{Total\:interest=Rs.2400}\end{cases}$

Formula used:-

${\boxed{\it{Simple\:interest\:(SI)\:=\:Prn\:}}}$

Now,

$\tt SI\:on\:1st\:part+ SI\:on\:2nd\:part=2400 \\\\ \rightarrow\sf PrN + Prn = 2400 \\\\\rightarrow\sf r(PN + Pn) = 2400 \\\\\rightarrow\sf r(6000 \times 4) + (8000\times 3) = 2400 \\\\\rightarrow\sf r(24000+24000) = 2400 \\\\\rightarrow\sf r\times 48000 = 2400 \\\\\rightarrow\sf r =\frac{2400}{48000} \\\\\rightarrow\sf r = \frac{1}{20} \\\\\rightarrow\sf r = \frac{1\times 100}{20 \times 100} \\\\\rightarrow\sf r =\frac{5}{100}$

$\rightarrow{\boxed{\sf {r = 5\%}}}$

$\therefore\bold{\underline{Rate\:of\:interest=5\%}}$