Incomes of A and B are in the ratio 9:10. Their expenditures are in the ratio 4:5. If they save Rs.6000 and Rs. 5000 respectively, what is the sum of their incomes?Question 3Answera.64,000b.57,000c.19,000/-d.38,000/

Let's solve this step by step:

Step 1: Let's assume the incomes of A and B as 9x and 10x respectively. Similarly, let's assume their expenditures as 4y and 5y respectively.

Step 2: According to the problem, the savings of A and B are the differences between their incomes and expenditures. So, we have:

9x - 4y = 6000 (This is because Income - Expenditure = Savings for A)

10x - 5y = 5000 (This is because Income - Expenditure = Savings for B)

Step 3: Now, we can solve these two equations to find the values of x and y.

Multiplying the first equation by 5 and the second equation by 4, we get:

45x - 20y = 30000

40x - 20y = 20000

Subtracting the second equation from the first, we get:

5x = 10000

So, x = 2000

Step 4: Substituting x = 2000 in the first equation, we get:

9*2000 - 4y = 6000

18000 - 4y = 6000

4y = 18000 - 6000

4y = 12000

So, y = 3000

Step 5: Now that we have the values of x and y, we can find the incomes of A and B:

Income of A = 9x = 9*2000 = 18000

Income of B = 10x = 10*2000 = 20000

Step 6: The sum of their incomes is 18000 + 20000 = 38000

So, the sum of their incomes is Rs. 38,000. Therefore, the correct answer is (d) 38,000.