Question

Salaries of Ajay and Vijay together amount to Rs.12,000. Ajay spends 80% of his salary and Vijay spends 90% of his salary. If their savings are the same, then what is Vijay’s salary?
A. Rs.2000
B. Rs.4000
C. Rs.8000
D. Rs.10000

Answer 1

Hint: We assume the salary of one of the people as a variable and use the sum to form an equation for the salary of the second person. Calculate the saving percentage by subtracting the percentage of spending from 100. Equate the percentage of savings of each person multiplied with their respective salary and equate them.
* We calculate the percentage of a number x as \[\dfrac{m}{{100}} \times x\].

Complete step-by-step solution:
Let us assume the salary of Ajay as \[x\]
The sum of salaries of Ajay and Vijay is Rs.12,000.
Then we can write salary of Vijay will be \[12000 - x\]
Now we are given Ajay spends 80% of his salary, then Ajay saves \[\left( {100 - 80} \right)\% = 20\% \] of his salary.
Since we have salary of Ajay as \[x\]
Then using concept of percentage we can calculate the amount saved by Ajay
\[ \Rightarrow \]Savings made by Ajay \[ = 20\% \times (x)\]
\[ \Rightarrow \]Savings made by Ajay \[ = \dfrac{{20}}{{100}}x\].................… (1)
Similarly Vijay spends 90% of his salary, then Vijay saves \[\left( {100 - 90} \right)\% = 10\% \]of his salary.
Since we have salary of Vijay as \[12000 - x\]
Then using concept of percentage we can calculate the amount saved by Vijay
\[ \Rightarrow \]Savings made by Vijay \[ = 10\% \times (12000 - x)\]
\[ \Rightarrow \]Savings made by Vijay \[ = \dfrac{{10}}{{100}}(12000 - x)\].............… (2)
Now we are given that they both have the same savings.
So, we equate the savings from both equations (1) and (2)
\[ \Rightarrow \dfrac{{20}}{{100}}x = \dfrac{{10}}{{100}}(12000 - x)\]
Cancel same factors from denominator on both sides of the equation
\[ \Rightarrow 20x = 10(12000 - x)\]
Cancel same factors from both sides i.e. 10
\[ \Rightarrow 2x = 12000 - x\]
Bring all variables to LHS of the equation
\[ \Rightarrow 2x + x = 12000\]
\[ \Rightarrow 3x = 12000\]
Cancel same factors from both sides i.e. 3
\[ \Rightarrow x = 4000\]
So, salary of Ajay is Rs.4000
We can calculate salary of Vijay as \[12000 - 4000 = 8000\]
So, salary of Vijay is Rs.8000

\[\therefore \]Option C is correct.

Note: Many students make the mistake of calculating the money spent as we are given a percentage of money spent. Then they subtract the money from assumed variables which exceeds the calculation and solution becomes lengthy and complex. We are given savings equal so we have to form an equation of savings.