Question

The difference of 2 years simple interst of Rs. 5000 given by two banks is Rs 25. What is the difference between the rate percent of these banks ?​

Answer 1

let the rate percent of these banks be x and y respectively......

Now,

According to question...

simple interest by 1 bank=5000×2×X/100

Simple interest by another bank=5000×2×y/100

their difference=25

100x-100y=25

x-y=1/4

x-y=.25

Hence the difference of rate percent is .25

Answer 2

Solution :

$\bf{\underline{\bf{Given\::}}}}}$

The difference of 2 years simple Interest of Rs.5000 given by two banks is Rs.25.

$\bf{\underline{\bf{To\:find\::}}}}}$

The difference between the rate percent of these banks.

$\bf{\underline{\bf{Explanation\::}}}}}$

Firstly, we know that formula of the Simple Interest :

$\boxed{\bf{S.I.=\frac{P\times R\times T}{100} }}}}$

$\bf{\red{\underline{\underline{\bf{1_{st}\:Case\::}}}}}$

$\bf{We\:have}\begin{cases}\sf{Principal\:(P)_{1}=Rs.5000}\\ \sf{Rate\:(R)_{1}=r_1}\\ \sf{Time\:(T)_{1}=2\:years}\\ \sf{Simple\:Interest\:=Rs.25}\end{cases}}$

So,

$\leadsto\sf{25=\dfrac{5000\times r_{1}\times 2}{100} }$

$\bf{\red{\underline{\underline{\bf{2_{nd}\:Case\::}}}}}$

$\bf{We\:have}\begin{cases}\sf{Principal\:(P)_{2}=Rs.5000}\\ \sf{Rate\:(R)_{2}=r_{2}}\\ \sf{Time\:(T)_{2}=2\:years}\\ \sf{Simple\:Interest\:=Rs.25}\end{cases}}$

So;

$\leadsto\sf{25=\dfrac{5000\times r_{2}\times 2}{100} }$

A/q

$\longrightarrow\sf{\dfrac{5000\times r_{1}\times 2}{100} -\dfrac{5000\times r_{2}\times 2}{100} =25}\\\\\\\longrightarrow\sf{\dfrac{10000\times r_{1}}{100} -\dfrac{10000\times r_{2}}{100} =25}\\\\\\\longrightarrow\sf{\dfrac{10000(r_{1}-r_{2})}{100} =25\:\:\sf{\big[Taking\:L.C.M\:of\:100\big]}}\\\\\\\longrightarrow\sf{10000\times (r_{1}-r_{2})=2500}\\\\\\\longrightarrow\sf{(r_{1}-r_{2})=\cancel{\dfrac{2500}{10000} }}\\\\\\\longrightarrow\sf{(r_{1}-r_{2})=\dfrac{1}{4} \%}$

$\longrightarrow\sf{\red{(r_{1}-r_{2})=0.25\%}}$

Thus;

The difference between the rate percent of these banks is 0.25% .