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: Let the salary of Ajay be x and salary of Vijay be y, which means $ x + y = 12000 $ and y will be equal to $ 12000 - x $ . And given that Ajay spends 80% of his salary and Vijay spends 90% of his salary, this means Ajay saves 20% and Vijay saves 10%. 20% of Ajay's salary is equal to 10% of Vijay’s salary. Use this information to find the salary of Vijay.

Complete step-by-step answer:
We are given that salaries of Ajay and Vijay together amount to Rs. 12,000 and Ajay spends 80% of his salary and Vijay spends 90% of his salary.
We have to find Vijay's salary when their savings are the same.
Let Ajay’s salary be x and Vijay’s salary be y. Their salary together amounts to Rs.12,000. This means $ x + y = 12000 $
This means Vijay’s salary can be written in terms of x as $ 12000 - x $
Ajay spends 80% of his salary and saves 20%; Vijay spends 90% of his salary and saves 10%.
As per the question, 20% of Ajay salary is the same as 10% of Vijay salary.
This gives $ 20\% ofx = 10\% ofy $
 $ \Rightarrow \dfrac{{20x}}{{100}} = \dfrac{{10y}}{{100}} $
Substitute y as $ 12000 - x $
 $ \Rightarrow \dfrac{{20x}}{{100}} = \dfrac{{10\left( {12000 - x} \right)}}{{100}} $
 $ \Rightarrow 20x = 10\left( {12000 - x} \right) $
 $ \Rightarrow 20x = 120000 - 10x $
 $ \Rightarrow 20x + 10x = 30x = 120000 $
 $ \therefore x = \dfrac{{120000}}{{30}} = Rs.4000 $
The salary of Ajay is x is Rs.4000 and the salary of Vijay is $ 12000 - x = 12000 - 4000 = Rs.8000 $ and both of their savings is Rs.800.
Hence, the correct option is Option C, Vijay’s salary is Rs.8000.
So, the correct answer is “Option C”.

Note: Above, we have solved the problem considering Ajay salary as x and Vijay salary as y. But we can also solve it by considering Vijay salary as x and Ajay salary as y, which gives us $ 10\% ofx = 20\% ofy $ , here y can be written as the same $ 12000 - x $ .