Question

A sum of Rs.15500 is lent out into two parts, one at 8% and another one at 6%. If the total annual income is Rs1969, the money lent at 8% is
\[(A)\text{ Rs 6500}\]
\[(B)\text{ Rs 7200}\]
\[(C)\text{ Rs 8400}\]
\[(D)\text{ Rs 9000}\]

Answer 1

Hint: we are given a total amount that was lent to be Rs1550. One part was lent at 8% and the other was lent at 6%. We are also given interest from both parts. So, we will calculate interest from both parts individually and then add them to equate it to Rs1060 so that we can calculate the amount that was lent. We will use a formula of simple interest which is \[SI=\dfrac{P\times R\times T}{100}\]where P is principal amount, R is rate of interest, T is time period.

Complete step by step answer:
Let us assume that money lent was Rs15,500, so money lent at 6% will become Rs(15500-x)
For money lent at 8% rate of interest:
Rate of interest=R-8
Principal value = x
We are given annual interest which means we have to calculate interest for one year only. Hence, time period, T= 1 year.
Formula for simple interest is given by\[SI=\dfrac{P\times R\times T}{100}\]
Where P is principal amount, R is rate of interest T is time period.
Putting values in above formula, we get
\[SI=\dfrac{x\text{ }\times \text{ }R\text{ }\times \text{ }T}{100}=\dfrac{2}{25}x\]……………………equation (1)
For money lent at 6% rate of interest:
Rate of interest =\[\text{R=6}\]
Principal value= Rs\[\left( 15500-x \right)\]
We are given annual interest which means we have to calculate interest for which means we have to calculate interest for one year only.
Hence, time period, T= 1 year.
Formula for simple interest is given by
\[SI=\dfrac{\text{P }\times R\text{ }\times \text{ }T}{100}\]
Putting values in formula, we have
\[S{{I}_{6\%}}=\dfrac{\left( 15500-x \right)\times \text{ 6 }\times \text{ 1}}{100}\]
       \[=\dfrac{\left( 15500-x \right)\text{ }\times \text{ 6}}{100}\]
       \[=\dfrac{46500-3x}{50}\]………………. equation (2)
We are given total interest at end of 1 year, hence, total annual income will be given by
\[S{{I}_{6\%}}+S{{I}_{8\%}}=Rs1060\]
Adding equation (1) and equation (2), we get
\[S{{I}_{6\%}}+S{{I}_{8\%}}=\dfrac{2}{25}x+\dfrac{46500-3x}{100}=1060\]
Taking L.C.M on left side,
\[\dfrac{4x+46500-3x}{50}=1060\]
\[\dfrac{x+46500}{50}=1060\]
Cross multiplying, we get,
\[x+46500=1060\times 50\]
\[x=53000-46500\]
\[x=Rs6500\]
As supposed earlier, money lent at a rate of interest 8% was x. Hence, money lent at rate of interest 8% was Rs6500.

So, the correct answer is “Option A”.

Note: Students should take care while calculating simple interest in terms of principal amount (x). Time period should be taken as 1 year as annual rate is given. And also, if there is 6% given in the question then it will be 6/100 and the 8% will be 8/100. Make sure when you solve the question sometimes, we forgot how to put the value of interest in the solution so keep in mind.