Question

The salaries of A and B together amount to Rs. 2000. A spends 95% of his salary and B, 85% of his. If now, their savings are the same, what is A’s salary?
A. Rs. 750
B. Rs. 1250
C. Rs. 1500
D. Rs. 1600

Answer 1

Hint: We will assume the salary of A to be x and the salary of B as y, so according to the question we will get that x + y = Rs. 2000. We have also been given that 5% of x = 15% of y. We will get a relation between x and y using these and we will find the values of x and y respectively and get the required answer.

Complete step-by-step answer:
It is given in the question that the salary of A and B together amount to Rs. 2000. A spends 95% of his salary and B spends 85% of his salary, but now their savings are the same and we have been asked to find the salary of A. Let us start by assuming the salary of A as x and that of B as y. So, we according to the condition given I the question, we get,
$x+y=2000\ldots \ldots \ldots \left( i \right)$
Now, it is given that A spends 95% of his salary, which means that he saves 5% of his salary. We can write that as $\dfrac{5}{100}x$. Again, it is given that B spends 85% of his salary, which means that he saves 15% of his salary, which can be written as $\dfrac{15}{100}y$. We know that as per the conditions given in the question, 5% of x is equal to 15% of y. So, we can write this relation as,
$\begin{align}
  & \dfrac{5}{100}\left( x \right)=\dfrac{15}{100}\left( y \right) \\
 & \Rightarrow 5\left( x \right)=15\left( y \right) \\
 & \Rightarrow x=3y \\
\end{align}$
So, we get that x is three times that of y, which means that the salary of A is three times more than the salary of B. We know that the combined salaries of A and B is Rs. 2000, which is represented as equation (i). So, we will put the value of x = 3y in equation (i) and get the value of y. So, we get,
$\begin{align}
  & 3y+y=2000 \\
 & \Rightarrow 4y=2000 \\
 & \Rightarrow y=\dfrac{2000}{4} \\
 & \Rightarrow y=500 \\
\end{align}$
So, we get the salary of B as Rs. 500. Now we will again put this value of y = 500 in equation (i). So, we get,
$\begin{align}
  & x+500=2000 \\
 & \Rightarrow x=2000-500 \\
 & \Rightarrow x=1500 \\
\end{align}$
So, we get the salary of A as Rs. 1500.
Hence the correct answer is option C.

Note: Many students misinterpret the question and think that 95% of the salary of A is equal to 85% of B’s salary and solve the entire question accordingly. Therefore, it is advised to read the question and understand it before solving the question.