Monthly income ratio of a and b is 5:6 and expenditure ratio is 4:5.If both have rs.500 in the end of the month then what is the income of a
Answers
the income of a is 2500 rs
Given:
The monthly income ratio of a and b is 5:6 and the expenditure ratio is 4:5. Both of them have Rs. 500 at the end of the month.
To Find:
The monthly income of a.
Solution:
The given problem can be solved using the concepts of ratio and proportions.
1. It is given that the ratio of monthly a and b is 5:6, and their expenditure ratios are 4:5. Both of them end up having 500 at the end of the month.
2. Let the monthly income of a and b be 5i,6i respectively. Let the monthly expenditure of a and b be 4e, 5e.
3. Monthly savings = Monthly salary - Monthly expenditures.
=> Savings of a and b are Rs. 500 each,
=> 500 = 5i - 4e ( Assume as equation 1),
=> 500 = 6i - 5e ( Assume as equation 2),
4. Solve equations 1 and 2 for the values of i and e.
=> Multiply equation 1 with 5 and Multiply equation 2 with 4,
=> 2500 = 25i - 20e ( Assume as equation 3),
=> 2000 = 24i - 20e ( Assume as equation 4),
Subtract equation 4 from equation 3,
=> 500 = 25i - 24i - 20e + 20e,
=> 500 = i,
=> i = 500.
5. The monthly income of a and b are 5x500, 6x500 i.e, 2500 and 3000 respectively.
Therefore, the monthly income of a is Rs. 2500.