Question

Arjun wants to invest Rs.15,000 in two types of bonds. He earns $12\% $ in the first type and $15\% $ in the second. His investment in $15\% $ bond, if he has a total earning of Rs$1,950$ is
(A) Rs$10,000$
(B) Rs$5,000$
(C) Rs$6,000$
(D) Rs$7,000$

Answer 1

Hint: In the given question we are given a total investment and the investment is divided into two parts and their ids earning on each part. The total earning that we earned from the investment is also given he has to find the amount of the second investment. In such types of problems, we divide the total investments into two parts by assuming one part as variable and the other part as the difference of total investment and first part. Then we make equations according to the questions if they have given the total earning then we find the earning from the percentage in terms of the variable assumed and then add both the earnings and equate it to the total earnings given and then solve the equation to find the value of a variable.

Complete step by step answer:
Step1: We are given an total investment of Rs$15,000$ and earns $12\% $ in the first type and $15\% $ in the second investment his total earning is Rs$1950$ so let us consider the first part of investment as $x$ then the investment in second part will be equal to $(15000 - x)$
Step2: now we will find the amount of earning on each part
Earning for first part is: $\dfrac{{12}}{{100}} \times x = \dfrac{{12x}}{{100}}$
Earning for second part is: $(15000 - x) \times \dfrac{{15}}{{100}} = \dfrac{{15(15000 - x)}}{{100}}$
Total earning given is Rs$1950$
Step3: We will add the earning and equate to the earning given equal to Rs$1950$
$\dfrac{{12x}}{{100}} + \dfrac{{15(15000 - x)}}{{100}} = 1950$
Taking L.C.M as $100$
$\dfrac{{12x}}{{100}} + \dfrac{{225000 - 15x}}{{100}} = 1350$
We will add the terms:
$ \Rightarrow \dfrac{{12x + 225000 - 15x}}{{100}} = 1950$
$ \Rightarrow \dfrac{{3x + 225000}}{{100}} = 1950$
On multiplying by $100$
$ \Rightarrow - 3x + 225000 = 195000$
On subtracting $225000$
$ \Rightarrow - 3x = - 30000$
Value of $x$ will be
$ \Rightarrow x = 10000$
Therefore we get the investment in $15\% $ bond by substituting the value of $x$ in $(15000 - x)$
We get $(15000 - 10000) = Rs5000$

Hence option (B) is correct.

Note:
Students mainly do mistakes in such type of questions in forming the equations. They also get confused about how to divide the investment. So they should assume one of them as a variable. This calculation is quite lengthy so be careful in performing calculations and do step by step. Always form the equation according to the requirement of the question.