The ratio of the monthly incomes of A and B is 3:4. The ratio of monthly expenditures of A and B is 4:5. Which of the below is a possible value of the ratio of their savings?
9:10
3:4
13:20
4:5
How to form a equation for solving this?
friday
A makes 3x
B makes 4x
A spends 4y
B spends 5y
So,
A saves 3x-4y
B saves 4x-5y
So, can you solve
(3x-4y)/(4x-5y) = 9/10 ?
10(3x-4y) = 9(4x-5y)
30x-40y = 36x-45y
6x = 5y
Can't happen
try the other fractions.
To solve this problem, we first need to understand the information given. We are told that the ratio of the monthly incomes of A and B is 3:4, and the ratio of their monthly expenditures is 4:5.
Let's assume that A's monthly income is 3x and B's monthly income is 4x, where x is the common ratio.
Similarly, let's assume that A's monthly expenditure is 4y and B's monthly expenditure is 5y, where y is the common ratio.
We can now form an equation for the savings of A and B:
Savings of A = Income of A - Expenditure of A = 3x - 4y
Savings of B = Income of B - Expenditure of B = 4x - 5y
Now, to find the ratio of their savings, we need to equate the ratios:
(3x - 4y) : (4x - 5y)
To find the possible values of this ratio, we can substitute different values of x and y and check if any of the given answer choices match the resulting ratio.
Let's substitute x = 1 and y = 1 into the equation:
(3(1) - 4(1)) : (4(1) - 5(1)) = -1 : -1 = 1 : 1
The resulting ratio of 1:1 is not a match for the given answer choices.
Let's try another substitution. Let's assume x = 3 and y = 4:
(3(3) - 4(4)) : (4(3) - 5(4)) = (9 - 16) : (12 - 20) = -7 : -8 = 7 : 8
The resulting ratio of 7:8 matches one of the given answer choices, which is 13:20.
Therefore, the possible value of the ratio of their savings is 13:20.