Question

A person lends 1500 rupees a part of it at 5% per annum and the other part at 9% per annum. If he recieves a total interest of 162 rupees at the end of 2years. Find out the amount lent at different rate of interest

Answer 1

$\sf\large\underline\blue{Let:}$

$\sf{\implies The\: first\:part=x}$

$\sf{\implies The\: second\:part=1500-x}$

$\sf\large\underline\blue{To\:Find:}$

$\sf{\implies The\: amount\:lent\:at\: different\:rate=?}$

$\sf\large\underline\blue{Solution:}$

• To calculate amount at the different rate of interest we have to find separately the simple interest from both part first and second. Then we will sum of both interest to find the amount:]

$\sf\small\underline\orange{Calculation\:for\: first\: part:}$

$\sf\large\underline{Here\:\:P=x\:\:,R=5\%\:\:,T=2\: years:}$

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

$\tt{\implies SI=\dfrac{x\times\:2\times\:5}{100}}$

$\tt{\implies SI=\dfrac{x}{10}}$

$\sf\small\underline\orange{Calculation\:for\:second\: part:}$

$\sf\large\underline{Here\:\:P=1500-x\:\:,R=9\%\:\:,T=2\: years:}$

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

$\tt{\implies SI=\dfrac{1500-x\times\:2\times\:9}{100}}$

$\tt{\implies SI=\dfrac{27000-18x}{100}}$

• Now calculate the value of x with help of given Interest in the question hence, the interest is equal Rs.162]

$\tt{\implies I\:_{1st}+I\:_{2nd}=162}$

$\tt{\implies \dfrac{x}{10}+\dfrac{27000-18x}{100}=162}$

$\tt{\implies \dfrac{10x+27000-18x}{100}=162}$

$\tt{\implies \dfrac{27000-8x}{100}=162}$

$\tt{\implies 27000-8x=16200}$

$\tt{\implies -8x=16200-27000}$

$\tt{\implies -8x=-10800\implies x=1350}$

$\sf\large{Hence,}$

$\sf\red{\implies The\: first\:part=Rs.1350}$

$\sf{\implies The\: second\:part=1500-x}$

$\sf{\implies The\: second\:part=1500-1350}$

$\sf\orange{\implies The\: second\:part=Rs.150}$